sanchezcarlosjr/2-2-fixed-point-iteration-illustration.ipynb

## 2-2-fixed-point-iteration-illustration.ipynb

      
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## notebook.ipynb
{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "2.2 Fixed-point iteration Illustration.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyOdcihzdMXOh9RxTvFORJt7",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/sanchezcarlosjr/c814b73dfcf4e415315fc170578d4807/notebook.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# 2 Solutions of Equations in One Variable\n",
        "##  2.2 Fixed-point iteration\n",
        "### Illustration\n",
        "By [Carlos Eduardo Sanchez Torres](https://twitter.com/CharllierJr)\n",
        "\n",
        "[Numerical analysis](https://www.notion.so/sanchezcarlosjr/Numerical-analysis-f774bbfddd834cf1beffda5e9e935ff8)\n",
        "\n",
        "Burden, Richard L., and J. Douglas Faires. Numerical Analysis. 7th ed. Belmont, CA: Brooks Cole, 2000. ISBN: 0534382169. Page 61."
      ],
      "metadata": {
        "id": "aDI5jvlKM5Ci"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The equation $x^3+4x^2-10=0$ has a unique root in $[1,2]$. The actual root is $1.365230013$.\n",
        "\n",
        "To obtain a solution with a fixed-point form\n",
        "$x=g(x)$, authors derive the functions shown here:\n",
        "\n",
        "$x=g_1(x)=x-x^3-4x^2+10$\n",
        "\n",
        "$x=g_2(x)=(\\dfrac{10}{x}-4x)^{1/2}$\n",
        "\n",
        "$x=g_3(x)=\\dfrac{1}{2}(10-x^3)^{1/2}$\n",
        "\n",
        "$x=g_4(x)=(\\dfrac{10}{4+x})^{1/2}$\n",
        "\n",
        "$x=g_5(x)=x-\\dfrac{x^3+4x^2-10}{3x^2+8x}$\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "XhrfRRR3vNk8"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Fixed-point iteration pseudocode\n",
        "To show all fixed-point iterations given an INPUT. It is an adaptation from the fixed-point iteration method which has a tolerance. \n",
        "\n",
        "INPUT: function $g_i$; initial approximation $p_0$; maximum number of iterations $N$.\n",
        "\n",
        "OUTPUT: solution $p$ or it returns Not a number (NaN).\n",
        "\n",
        "```\n",
        "fixed_point(g,p0,N)\n",
        "  if N == 0\n",
        "    return p0\n",
        "  for i <= N\n",
        "     p = g(p0)\n",
        "     if p is complex\n",
        "       return NaN # Unsuccessful method\n",
        "     if p is underflow or p is overflow\n",
        "       return NaN # Unsuccessful method\n",
        "     p0 = p\n",
        "  return p # Successful method\n",
        "```\n",
        "\n",
        "So, we can apply our fixed point method as shown below:\n",
        "```\n",
        "show_table(g,p0,N):\n",
        "  list=[]\n",
        "  for i <= N\n",
        "    list.append(fixed_point(g,p0,N))\n",
        "\n",
        "data=[\n",
        "  show_table(g1,1.5,30),\n",
        "  show_table(g2,1.5,30),\n",
        "  show_table(g3,1.5,30),\n",
        "  show_table(g4,1.5,30),\n",
        "  show_table(g5,1.5,30)\n",
        "]\n",
        "show_dataframe(data, [\"g1\", \"g2\", \"g3\", \"g4\", \"g5\"])\n",
        "```\n",
        "\n"
      ],
      "metadata": {
        "id": "KR2k_9Kyr_tZ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "# 100 linearly spaced numbers\n",
        "x = np.linspace(1,2,100)\n",
        "p=1.365230013\n",
        "\n",
        "# plot the function\n",
        "plt.ylabel('$g_1(x)=x-x^3-4x^2+10$',fontsize=20)\n",
        "plt.xlabel('$x$',fontsize=20)\n",
        "plt.plot(x,x-x**3-4*x**2+10, 'r')\n",
        "plt.plot(p,p, '-o',linewidth=5)\n",
        "plt.grid(True,linewidth=5)\n",
        "# show the plot\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "nXOvzKagSBMG",
        "outputId": "7cee5451-7eae-4857-9911-47e6989e0db4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 301
        }
      },
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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wItkr6QnIzP5mZn0A3H0OoTxbJKM0qr916dvX/heefVaFCiJJkIoR0MXAURvfuPvHKTiHSEpd0X0vtq5V43fbtt4CrvjgxTCbwhFHhJVaRaTS4pqKx8z6VbDpXsXbuvujcUUlErH8No0BGDZxISu//ZFG9bfmiu57kX9jdxjeCQYPhrZt4ayzwjQ/IhK3eOeCGwFs7tqDEy67dSY8mOqAEpBknPw2jX9LRL9z3nmhXPvGG+Hee2HMGPbo3ZvFxxyD16q1aXsRKVVlJiP9HngQ+KGUfQYMJiz29p8E4hJJb9tvD3feCX/9K1x2GfuNHEmzSZNY0K8fX7Rrp6UfRCog3gTUl7B66PHAGbFKt98xs8HA2+5+QxLiE0lve+8Nzz/PzMGD2e/RR+lw88180bYtC848M+rIRNJeXEUI7v4kcADwCTDNzO4ws9opiUwkg3zZrh1T776b+f368YcPPqDrhRfCFVeAlnEXKVPcVXDuvszdjyTM+3Ye8E5sRVGRas1r1mTxcccx+f77Wda1KxQUQIsWMGqUlgYXKUUiMyHcDbQj3AuaYWa3mpnuwEq193P9+swZMADeeAOaNQuzKxxySJjqR0R+k+iCdO8DBwG3ApcD77D5KjmR6uHAA+H11+HRR2HRIsjNDRV0//1v1JGJpIVkLEj3q7sPJpRd12IzS2GLVCtbbAFnnBHWH7rgAnjoIdhrLxgxQpflpNpL2kwI7v4GYRmG7YELk3XcyjKzo81soZktMrOrStlf28z+Gdv/hpaOkJSqXx/uvhveeSdUzp19NnTsqMtyUq2ZZ+GcVmZWA/iQMCXQcuAt4GR3f69Ym/OAA9y9v5mdBPRy9z+Vd9ycnBwvKChIYeRSLbjTZNo09n38cWqvXs3So4/m/VNO4Zc6daKOTCQl8vPzZ7t7bsntKZsNO2LtgUXuvtjdfwbGAHkl2uQBj8d+fwY4wkxPD0oVMGN5165MufdelvTsSbOJEzn8/PNpMnWqJjmVaiVbE1BjYFmx98tj20pt4+7rgdXADiUPZGbnmFmRmRWt0TMdkkTr69Rh/tlnM+2OO/hhl11od/fddBo0iDrLlm3+wyJZIFsTUNK4+3B3z3X33Lp160YdjmShNbvvzmu33sqc886j7ief0PWSS9jniSeosW5d1KGJpFS2JqAVQNNi75vEtpXaxsxqAvWAVVUSnUhJW2zBJ926MeW++1h+yCG0GDuWrhdcwE6zZ0cdmUjKZGsRQk1CEcIRhETzFvBnd3+3WJvzgf2LFSEc7+4nlnfc3NxcLyoqiiuWwsLCTbbl5ZW8HZVd1OcgoT6/8gqcey68/z706QN33QWNGiUQYfLp7xxkc5+T1V8zS20RgpmNMrNbk3W8RMTu6QwAJgLvA0+7+7tmdqOZHRdr9giwg5ktAi4FNinVFonMoYeGBe9uvhn+8x/YZx+47z749deoIxNJmmRegvsLm1aaRcbdJ7h7C3ffw92HxrYNdvd/x37/yd37uHuOu7d398XRRixSwpZbwrXXwoIFcNBBMGAAdOoEc+dGHZlIUmTrPSCR7LHHHjBxIjz5JCxeDO3awZVXwg+lLcklkjmUgEQygRmccgp88EGY3PT222H//WHy5KgjE6k0JSCRTPKHP8Ajj8DLL0ONGnDUUSEhrVIBp2QeJSCRTNS1a7gXdM01MHp0KFIYM0YzKUhGUQISyVRbbw1Dh8Ls2dC8OZx8Mvzxj6CZFCRDKAGJZLoDDgjrDt15J0ydCvvuCw88oOUeJO0pAYlkgxo14OKL/1eyfd55cNhh8NFHUUcmUiYlIJFs0rw5TJoUVmGdPz+MjoYNg/Xro45MZBNKQCLZxiyswvruu3D00TBwYFj8bsGCqCMT+R0lIJFs1agRjBsXquOWLIG2bcPUPr/8EnVkIkByE9CnbDrjtIhEyQz+9Cd47z04/ni47jpo317T+UhaSFoCcvdm7n5Uso4nIknUoEEYCY0bBytXQm4u3HijRkMSKV2CE6lOevUKo6ETT4Trrw+joXnzoo5KqiklIJHqZocd4KmnYPz4/42Ghg5VpZxUOSUgkeoqPz9UyvXuDYMGQYcO4b1IFVECEqnOdtwR/vEP+Ne/4JNPQqXcsGFa+E6qhBKQiMAJJ4TRzzHHhOeGunSBRYuijkqynBKQiAQ77QRjx4aF7957D1q1gvvv1wzbkjIVSkBmtp+ZnW1m+8betzSzh81slJl1S22I8TGzYWb2gZnNM7PxZla/jHZLzWy+mc0xs6KqjlMkLW1c+G7BAjjkEDj//DCbwgo94ifJt9kEZGY9gbeB24DZZtYDeAVoBjQGJpjZkakMMk4vAfu5+wHAh8DV5bTt6u6t3T23akITyRCNG8MLL4RZtadPh/32C/eKRJLIfDPDazN7HXjZ3QeZ2UnA/cAD7n5tbP+tQDt3T6uREICZ9QJOcPdTStm3FMh1968rerycnBwvKChIYoQi6W/blStpe/fd/GHhQpZ37sy8v/6VX7bbLuqwJIPk5+fPLu0f+hW5BLcvMDL2+9PAdsAzxfY/BRyQaIAp0g94oYx9Dkwys9lmdk4VxiSSUdY2asT0W27h/VNOodHMmXS96CIazJkTdViSBSpahLABwN03AD8Bq4vt+w6ol+S4ymVmk81sQSmvvGJtrgXWExJkaTq7e1ugB3C+mXUp41znmFmRmRWtWbMm6X0RyQReowYf9unDq7ffzvpttqHjkCHsN2IEW6xbF3VoksFqVqDNUmBPYHHs/cGEiUc3agp8ntywyufu5d5zMrPTgWOBI7yMa4zuviL280szGw+0B14tpd1wYDiES3CJRS6S2VbvsQfTCgpo+cQT7PHcc+w0Zw6zL72U1bvvHnVokoEqMgJ6CNhy4xt3X+DuxefsOAaYluS4Ks3MjgYGAse5+w9ltNnWzLbb+DvQDdBiKSIVsKF2bRacdRavX389tdaupcvAgeSMG6eHVyVumy1CyDRmtgioDayKbZrl7v3NrBEwwt17mtnuwPjY/prAaHcfurlj5+bmelFRfBXbhYWFm2zLy8srpWX2UJ+D6tDnWmvW0Pr++2k0axZf7bcfDSZMgKZNow4tZarb3zlZ/TWzUosQKnIJLqO4e04Z21cCPWO/LwZaVWVcItnol7p1eevKK9l1yhT2HzEiPLz60EPQp0/UoUkGqPRMCGZ2SzIDEZEMZcanRx7JtDvvhD33DEs99OsH338fdWSS5hKZiucqM7s/aZGISEZb27BheGh10CB4/HFo0wbeeivqsCSNJZKARgH9zWy0mZV6Kc/MOsUeZBWR6qBWLbjpJpg6Fdatg44d4bbbYMOGqCOTNFTpBOTupwN3AicBhWa21cZ9ZranmY0jlDUflGiQIpJhunSBuXPDCqxXXw1HHRUWvxMpJqHZsN39MmAQ4WHOSWbWwszuI5Q05wOzCSXOIlLdbL89/POfMGIEzJoFBxwA//lP1FFJGkl4OQZ3vwW4AOgMvA/0Jzy02sfd27v7lETPISIZygzOPBNmzw7l2ccdBxdeCD/9FHVkkgYSSkAW9AUu3biJMCtCZ3cfm2hwIpIl9t47jIIuugjuuScs//3BB1FHJRFLpAy7FzAfeAxoSFiu4TJgF2Cyme2UlAhFJDvUrg133RUuwy1fDu3awciRWvCuGktkBDQW2JtQDdfC3a9x9zuBU4GWwAwza5ZwhCKSXY49NhQoHHggnHEG9O0L330XdVQSgUQS0EtAW3c/w92Xb9zo7qOBXkAjYPrGVVRFRH7TuDFMmQI33ACjR4fRkJZ4qHYSKcPu7u7zytg3AegO1CGsnioi8ns1asDgweGZobVrw32h++/XJblqJOEquLK4+3TgMOCXVJ1DRLJAly5h9HP44XD++WEeudWrN/85yXgpS0AA7j6HUJ4tIlK2Bg3guefg9tvh2WehbVuIc+Z5yTwpTUAA7v5xqs8hIllgiy3giivg1Vfhl1/CND733KNLclks5QlIRCQuHTvCO+9A9+7hodUTT9QluSylBCQi6WeHHaCwMFySGz8+VMm9807UUUmSKQGJSHraeEnulVfC1D0HHwzDh+uSXBZRAhKR9NapUxj9HHoo/PWvcNppoWxbMl7SEpCZjTKzW5N1PBGR3zRoABMmhAdXn3wSDjpIc8llgWSOgP4C5CXxeJViZkPMbIWZzYm9epbR7mgzW2hmi8zsqqqOU0TitPHB1UmT4Msvw1Q+Tz8ddVSSAPMkXU81sw3AB+7eMikHrHwcQ4Dv3f2OctrUAD4EjgKWA28BJ7v7e+UdOycnxwsKCpIYrYhUxlarVpE7bBg7fPABHx97LO+edhpeq1bUYUkZ8vPzZ7t7bsnt1fUeUHtgkbsvdvefgTGkwehNRCrmpx12YMbNN/PxH//IHs89R+dBg9jq66+jDkvilK0JaICZzTOzR81s+1L2NwaWFXu/PLZtE2Z2jpkVmVnRmjVrUhGriFSC16zJgjPP5K3LL6fuJ59w2GWXseO8UqenlDSVkQnIzCab2YJSXnnAA8AeQGvgMyCha2buPtzdc909t27dukmIXkSSaWXnzrwybBg/b7cdHYcMIWfcOJVqZ4iaUQdQGe5+ZEXamdnDwHOl7FoBNC32vklsm4hkoO+bNuXVYcNofc897DtqFNt/+CHvXHgh67fZJurQpBzZWITQ0N0/i/1+CXCQu59Uok1NQhHCEYTE8xbwZ3d/t7xj5+bmelGcEyQWFhZusi0vL7tvN6nPgfocAXe4804YOBBycmDcOGiZvK+ktOxzCiWrv2ZWbYoQbjez+WY2D+gKXAJgZo3MbAKAu68HBgATgfeBpzeXfEQkA5jBpZeGxe6++SY8LzR2bNRRSRky8hJcedz91DK2rwR6Fns/AZhQVXGJSBU69FB4+2044YTwGjgQhg6Fmln3lZfRsnEEJCISlv2eNg369w+TmvboAatWRR2VFKMEJCLZq3ZteOABeOSRsM5Qbm5YfVXSQjIT0KeokkxE0lG/fvDaa7B+fVhvaPToqCMSkpiA3L2Zux+VrOOJiCRV+/Ywe3aYQ+6UU+Dyy0NCksjoEpyIVB877QSTJ8OAAVBQAEcfrftCEVICEpHqpVYtuOceeOyxcFnuwANBU/hEQglIRKqn008PhQnr1oXVVp95JuqIqh0lIBGpvg46CIqKoFUr6NMHBg2CDRuijqraqHQCMrNbkhmIiEgkGjaEqVPhzDPDw6q9eoFmvq8SiYyArjKz+5MWiYhIVGrXhocfhr//HZ5/PlySW7Qo6qiyXiIJaBTQ38xGxyb33ISZdTKz1xM4h4hI1TCDCy6AiRPh889D2faUKVFHldUqnYDc/XTgTuAkoNDMttq4z8z2NLNxwKvAQYkGKSJSZY44At58M1ya694d7r1X6wulSEJFCO5+GTAI6AFMMrMWZnYfsADIB2YD3RKOUkSkKu2xB8ycCT17hlFR//7wyy9RR5V1Eq6Cc/dbgAuAzoSlDfoDi4E+7t7e3TWGFZHMU7cujB8PV10Fw4dDt27UUnFCUiWUgCzoC1y6cRPwOdDZ3bUIh4hktho14NZb4YknYOZMDr3iCrZbtizqqLJGImXYvYD5wGNAQ+A24DJgF2Cyme2UlAhFRKL2l7/AtGnUWLeOQ668kp1mz446oqyQyAhoLLA3oRquhbtf4+53AqcCLYEZZtYs4QhFRNJBhw68MmwYa3femQ5Dh7L7f/6j4oQEJZKAXgLauvsZ7r5840Z3Hw30AhoB081s3wRjFBFJCz81aMD0W2/ls/bt2f+RR2j1wAMqTkhAImXY3d291Bn8YstddwfqAK9U9hyVYWb/NLM5sddSMyt19anYvvmxdkVVGaOIZK5ft9qKtwYO5MPevWk2aVKYUfubb6IOKyOZp3AIaWatgRfcvWHKTlL++QuA1e5+Yyn7lgK57v51RY+Xk5PjBQUFSYxQRDJZ06lTaX3fffyw007MGjSItY0aRR1SWsrPz5/t7rklt6d0MlJ3n0Moz65yZmbAicA/oji/iGS/ZV27MuPGG6n1/fd0ufJKdliwIOqQMkrKZ8N2949TfY4yHAJ84e4flbHfCQ/Pzjazc8o6iJmdY2ZFZla0Rs8AiEgJ/23Zkldvv5119erRccgQmr78ctQhZfy1xzYAABFnSURBVIyMXI7BzCab2YJSXnnFmp1M+aOfzu7eljCLw/lm1qW0Ru4+3N1z3T23bt26SeyFiGSLH3bZhVdvu41VLVvS9u9/Z58nn9SyDhVQ6iSi6c7djyxvf2xy1OOBduUcY0Xs55dmNh5oT5i7TkQkbuvr1GHm4MEc8NBDtHjmGbb5/HPeueACNtSuHXVoaSsjE1AFHAl8ULw8vDgz2xbYwt2/i/3eDdikUKGk+vXrk5eXt7lmv1NYWLjJtniPkWnU50B9zj4V6vPxx8Mdd9Bk4ECa/PorFBZCgwZVFGFypfpvnJGX4CrgJEpcfjOzRmY2IfZ2Z8IzSnOBN4Hn3f3FKo5RRLKRGVxxRVji+513wqqrH3wQdVRpKeEEZGZ5ZvZoWe+j4O6nu/uDJbatdPeesd8Xu3ur2Gtfdx8aTaQikrV694ZXXoG1a8MCd9OmRR1R2knGCKg1cFo570VEqqf27eGNN8LaQt26wahRUUeUVrL1EpyISHpo1gxefx0OOQROOw1uvFFzyMUoAYmIpFr9+vDCC9C3L1x/PfTrpznkyN4qOBGR9LLlljByJDRvDjfcAMuXh0KFevWijiwyGgGJiFQVMxgyBB57LBQldOkSElE1pQQkIlLVTj8dJkyAJUugQweYV+rCAllPCUhEJApHHQWvvRYKEjp3hilToo6oyikBiYhEpVUrmDULdt0VevSAJ5+MOqIqpQQkIhKlpk1h+nTo1AlOPRVuu63alGkrAYmIRK1+fXjxRTj5ZLj6ahgwAH79NeqoUk5l2CIi6aB27XAJrkkTGDYMPv88vN9666gjS5lkjIBWA5+W815ERCpiiy3g9tvhrrtg/Pgwfc9//xt1VCmTcAJy97vcvXlZ70VEJE4XXQRjxsCbb4YpfJYtizqilNA9IBGRdHTiiTBxYnhQ9eCD4d13o44o6ZSARETS1WGHhWeFNmwIzwq99lrUESWVEpCISDo74ACYORN23jncEyplldJMpQQkIpLudtstPCvUqlVY8nvEiKgjSgolIBGRTLDjjmG6nu7d4eyz4eabM/6BVSUgEZFMse224RLcqafCddeFarkNG6KOqtIyMgGZWR8ze9fMNphZbol9V5vZIjNbaGbdy/h8czN7I9bun2a2ZdVELiKSoFq1wrpCl14K99wDp5wCP/8cdVSVYl7JIZyZHQUcBXQBdgV2BH4EvgTmAC8D/3b3FckJ9Xfn3gfYADwEXO7uRbHtLYF/AO2BRsBkoIW7/1ri808D49x9jJk9CMx19wc2d96cnBwvKChIbmdERCrDnZzx49l31Ci+bN2aN6+6il+32irqqEqVn58/291zS26PawRkZtuY2VVmtgR4Ebic8GVfn5B41gO7A72B+4AlZjbWzA5OtAPFufv77r6wlF15wBh3X+fuS4BFsfiK98GAw4FnYpseB/KTGZ+ISMqZsej443lnwAAazJtHx8GDqbVmTdRRxaXCCcjM+gEfAbcQRjo3EEZA9d19G3dv4u47EOaXawn0A8YCPYDpsUtduya7AyU0Boo/Mrw8tq24HYBv3X19OW1+Y2bnmFmRmRWtybA/rohkv0+PPJI3Bw6k3pIldL72Wrb6+uuoQ6qweEZAI4A3gIPcvaW73+juU9z9d9/KHnzg7iPd/WRgF+BioDNwekVPZmaTzWxBKa+8OGJOmLsPd/dcd8+tW7duVZ5aRKRCPu/QgVmDB7P1119zyNVXs+2KpN/5SIl4ElCuux/v7m/FcwJ3X+Pu9wB7AE/H8bkj3X2/Ul7lPYW1Amha7H2T2LbiVgH1zaxmOW1ERDLK1/vvz4ybb6bGzz9zyDXXUG/x4qhD2qxKFyGkAzObxu+LEPYFRvO/IoQpwJ6lFCH8CxhbrAhhnrvfv7nz5ebmelFRUVwxFpby1HJeXpUO4qqc+hyoz9knI/q8cGFY7nv1anjuuTCZaSUlq79mlngRQokD3lLZzybKzHqZ2XLgYOB5M5sI4O7vEkZZ7xGKJM7fmHzMbIKZNYod4krgUjNbRLgn9EhV90FEJCX22gtmzICGDcPUPRMmRB1RmRJ5DugqM9vsqCEV3H18rOihtrvv7O7di+0b6u57uPte7v5Cse093X1l7PfF7t7e3XPcvY+7r4uiHyIiKdG0aZi4tGVLyMuDf/4z6ohKlUgCGgX0N7PRxe6n/I6ZdTKz1xM4h4iIVEaDBvDyy9CxY1jq+6GHoo5oE5VOQO5+OnAncBJQaGa/PQFlZnua2TjgVeCgRIMUEZFKqFcPXnwRevaE/v3DUt9pJKGpeNz9MmAQ4VmfSWbWwszuAxYQHu6cDXRLOEoREamcrbeGcePgT3+CgQNh0KC0mcS01Etn8XD3W8xsNXAP8H5s84fAIHcfm+jxRUQkQVtuCU89BdttB0OHwpo1cNddsEW004EmlIBi09qcCly6cRPwGdDZ3VclGJuIiCRLjRowfDjUrQt/+xt8911YV6hGjchCqnQCMrNewE3APsA64DbgK+AOYLKZdXf3L5MSpYiIJM4M7rgjjIRuuAHWroUnnwwjpAgkMgIaS5iRehRwnbsvBzCzL4DHgBlmdpS7L004ShERSQ4zGDIkJKHLLw9J6Jlnwr2iKpbIBcCXgLbufsbG5APg7qOBXoSZCKbHZicQEZF0ctlloTT7hRfg2GPh+++rPIREyrC7u/u8MvZNALoDdYBXKnsOERFJoXPOgVGj4JVXwlLf335bpadPWQmEu08HDgN+SdU5REQkQX/5S5gp4a234IgjYFXV1Y/Fsx5Q3BcI3X0OYRmGSh9DRERSrHdvKCyE996Dww6DL76oktPGMwJaYmYXmVnteE7g7h+bWSszKySsoCoiIummRw94/nlYvBi6dIHlyzf/mQTFk4AmAn8DPjOzB8ysa3kjGjPb3czONbOZwNtAK2BqYuGKiEjKHH44TJoEn30GXbqwdYpHQhVOQO5+GtABKALOASYDq81srpm9aGb/MLPxZvZqrBT7I+A+oDlwLbBX7L6QiIikq06dYMoU+OYbOg8axLaffZayU8VVhODub7l7N2BvYBgwF2hJmO/tT0Ae/7vnMw74M9DU3W/TkgciIhniwANh6lRq/PQTna69ljopuhxXqSo4d//I3a9y9wOBesBeQEegDdA4tkZPH3cf4+6qghMRyTStWzPj5puxDRvodO21bLdsWdJPkXAZtrv/EEtIs9x9rrunbrwmIiJV5rvddmPG0KGsad6cdXXrJv34Cc+GLSIi2ev7xo2ZOWRISo4d7VzclWRmfczsXTPbYGa5xbYfZWazzWx+7OfhZXx+iJmtMLM5sVfPqoteREQAzKtwYSIzawrc4O79EjzOPoSJUB8CLnf3otj2NsAX7r7SzPYDJrp741I+PwT43t3viOe8OTk5XlBQkEjoIiLVTn5+/mx3zy25vapHQH8ATkv0IO7+vrsvLGX7O+6+Mvb2XWDreB+cFRGRqpHUe0Bm1nczTXZN5vk2ozfwdjnl3wNi8RYBl7n7N6U1MrNzCM890aBBg5QEKiJSHSW7CGEk8ANQ1nW9eOaemwzsUsqua929cDOf3Rf4P8LzSaV5gLCYnsd+FgClXhZ09+HAcAiX4CoUvIiIbFayE9BK4EJ3H1faTjNrDcyuyIHc/cjKBGBmTYDxQF93/7iMY39RrP3DwHOVOZeIiFReshPQbKAtYRaE0jhgST7nb8ysPvA8cJW7zyinXcNizyv1AhZU5Pj169cnLy8vrpgKCzcdrMV7jEyjPgfqc/apbn1OdX+TXYRwB1DmFz+wCOia6EnMrJeZLQcOBp43s4mxXQOAHGBwsRLrnWKfGVGsZPv2WKn2vFg8lyQak4iIxKdKy7AznZl9BXxSyY/vCHydxHAygfpcPajP2S/R/u7m7ptUcVU6AZnZXMIyCxtfc9x9bQIBZjUzKyqtDj6bqc/Vg/qc/VLV30TuAe0O7A9sLL12M/uI3yelt919dWIhiohINkrkHlA94ElCUcEywtIM9YCTgdsJ6wWtMrMiM7vEzLZJNFgREckeiSSgK4ETgCPcvZm7t3P3RsA+wOOExPQh0IzwnM27ZnZAgvFmsuFRBxAB9bl6UJ+zX0r6m8g9oKXAy2XN62Zm5wPXAQcChwH3A98DB7j7V5U6qYiIZI1ERkA7A2UuGO7u9xHKrq9w9ycIz9vsjEqeRUSExBLQYuCIzbSZDhwH4O6TY+//mMA505qZPWpmX5pZqQ+2WvB3M1tkZvPMrG1Vx5hsFejzKbG+zjez182sVVXHmGyb63Oxdgea2XozO6GqYkuVivTZzA6LPXv3rpm9UpXxpUIF/tuuZ2b/MbO5sT6fUdUxJpOZNTWzqWb2Xqw/F5XSJqnfYYkkoCeAdmZ2TTltduH387nNAZoncM50NxI4upz9PYA9Y69zCHPSZbqRlN/nJcCh7r4/Yd69bLh2PpLy+4yZ1SDMRzipKgKqAiMpp8+xWUjuB45z932BPlUUVyqNpPy/8/nAe+7einCbocDMtqyCuFJlPWFi5pZAB+B8M2tZok1Sv8MSSUB3Am8CN5nZ2JKZ0My6An8iVMht9EuC50xr7v4q8N9ymuQBozyYBdQ3s4ZVE11qbK7P7v56sZnGZwFNqiSwFKrA3xngAmAs8GXqI0q9CvT5z8A4d/801j7j+12BPjuwnZkZUCfWdn1VxJYK7v6Zu78d+/074H2g5HpqSf0Oq3QyiC1zcATwD8L9nbdiw9XZZraYUIZdG7ir2Mf2AFZV9pxZoDG/T8jL2fQPnM3OBF6IOohUM7PGhP8nsmGEW1EtgO3NbFrsO2BzS7Nkg3sJVb8rgfnARe6+IdqQksPMmgFtgDdK7Erqd1hCoxF3/8Hd/wJ0BEYTViltAzQlZM9TY8UImFkDoDubdkiqgdiI+ExC+X62uwu4Mlu+jCqoJtAOOIbw//l1ZtYi2pBSrjvhtkIjoDVwr5nVjTakxJlZHcLo/WJ3X5PKcyVlNuzYUGwWQGwF0l/dveRQdBWhJPvnZJwzQ60gJOeNmsS2ZbXY818jgB7uXh1GwLnAmHBlhh2Bnma23t2fjTaslFoOrIpNx7XWzF4FWhGeBcxWZwC3eXiWZZGZLQH2JtyayEhmVouQfJ4qY1mdpH6HJf1+jLuvKyX54O4b3H2Bu2fzf5Cb82+gb6ySpAOwutiyEFnJzHYlLM9xanX527t789jD2c2AZ4Dzsjz5ABQCnc2sZmzWk4MIV0Gy2afEKoHNbGdgL0J1cEaK3ct6BHjf3f9WRrOkfoclez2gas3M/kGohtkxtlzE9UAtAHd/EJgA9CQ8H/UD4V9QGa0CfR4M7ADcHxsRrM/0SRwr0Oess7k+u/v7ZvYiMI9wKX6Eu1dona10VYG/803ASDObT5j55Up3z+QZsjsBpwLzzWxObNs1wK6Qmu8wLccgIiKRyNqSaBERSW9KQCIiEgklIBERiYQSkIiIREIJSEREIqEEJCIikVACEhGRSCgBiYhIJJSAREQkEkpAIhnIzCaZmZtZ7xLbzcxGxvbdFlV8IhWhqXhEMlBsafO3gYXA/u7+a2x7AXApMNzd/xphiCKbpRGQSAZy97nAE4QF0U4FMLNrCMnnaeDc6KITqRiNgEQylJk1Jay38zlQANwDTASOc/fqvO6WZAglIJEMZma3AlfF3r4OHOXuP0QYkkiF6RKcSGb7qtjvZyr5SCZRAhLJUGb2Z+AOwiU4gIsiDEckbkpAIhnIzHoCI4EFwAGEarizzGyvKOMSiYcSkEiGMbPOwDPAcqC7u38FDAJqAv8XZWwi8VARgkgGMbPWwDTgR6Czu39cbN9bQC7Qxd1fiyZCkYrTCEgkQ5hZDvAi4ISRz8clmlwd+zmsSgMTqSSNgEREJBIaAYmISCSUgEREJBJKQCIiEgklIBERiYQSkIiIREIJSEREIqEEJCIikVACEhGRSCgBiYhIJJSAREQkEv8PCS0ucV4tJPUAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "# 100 linearly spaced numbers\n",
        "x = np.linspace(1,2,100)\n",
        "p=1.365230013\n",
        "\n",
        "# plot the function\n",
        "plt.ylabel('$g_2(x)=(\\dfrac{10}{x}-4x)^{1/2}$',fontsize=20)\n",
        "plt.xlabel('$x$',fontsize=20)\n",
        "plt.plot(p,p, '-o',linewidth=5)\n",
        "plt.plot(x,(10/x-4*x)**0.5, 'g')\n",
        "plt.grid(True,linewidth=5)\n",
        "\n",
        "# show the plot\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "V9E1GCX1SsNr",
        "outputId": "ac8ef912-6423-452f-9ca1-d8065667156a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 288
        }
      },
      "execution_count": 59,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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8vO5h7ltzH/N3zlcxEskEonEl1IvQiqsigTgl1yn0vKAn63qu4/aSt7Pj0A4eW/8Yd6++m692fKXJUkUClK7RceElvlOjQtJj3X10etoVORG5c+amSeEmXHrapXz5+5e8v/V9Bm0YxIfPf8iD9R+kbeW25MyhyVJFoim9/8e9DKR0T8MJfQ5Uj9BwagdUhCQwOS0nFxe6mIsKXsRXO77io70fcePEG3l45sM8UO8B2p/bnlxxuYKOKZItROLPvj3Ai8De4+wzoD+wCPgwAm2JRMzRyVIHdRjE5JWTGTBrAJ0/6MyAWQO4v+79dKzWkdw5cwcdUyRLS+9nQjcBR4DWwGfu/u9jvh4OH7co6fZ0tikSUTksB1dVvIqFXRYypd0UipxahK7/6Uris4k8981z/Hnoz6AjimRZ6SpC7v4GcC6wEZhhZk+Zmf50lJhkZjQ7qxlzO89l+o3TSYhPoMe0HpQZVoZn5j7D3oPHu9gXkfRI9+g4d//R3S8DehOal+2/ZlYr3clEAmJmNCrXiFkdZ/FFhy+oWLgid0+/mzLDyjB4zmD2HNgTdESRLCOS0/YMA84j9NnQHDMbGF5mQSQmmRkNExryeYfPmdVxFlWLVOXeT++lzLAyPDH7CXbv3x10RJGYF+mVVVcQWi5hINAH+C8pj54TyfTql67P9PbT+arTV9QsXpMHPnuAhGEJPDrrUXbt10q8Iicq4g+ruvthd+9PaEh2LlKY5VokltQ+szbTbpjG17d8Te2Sten3RT8ShiYwYOYAdv65M+h4IjEnw2ZMcPevCa0jVBDomVHtiAShVolaTLl+CvNvnU+9UvXoP6M/CcMS+PeMf7Pjzx1BxxOJGRk6bU/4qminu2uMq2RJNYvX5IN2H7Cwy0IalG7AwzMfJmGoipFIakV1Fm2RrKpGsRpMum4S/73tv1xS5hIVI5FUUhESiaBqRasxoe2E4xYjfWYk8ncqQiIZIGkxurjMxaFiNCyBR2Y+omIkkoSKkEgGqla0GhPbTmRRl0U0KN2Ah2Y8RJlhZTS0WyRMRUgkCqoXq86k6yaxsMtC6pWq97+h3Y9/+bgeepVsLcOKkJmNNbOBGXV+kVhUo1gNPmj3AQtuXUCdM+vw4OcPUnZ4WQbPGcwfB/4IOp5I1GXkldCNQMsMPL9IzDqv+HlMuX4KX9/yNTWL1+TeT++l7PCyPDP3GfYd3Bd0PJGo0e04kQDVKlGLaTdMY/bNs6lyRhXunn435YaXY8Q3I9h/aH/Q8UQynIqQSCZQt1RdPr3pU2Z0mEFioUTumHYH5Z8tz6iFozh4+GDQ8UQyjIqQSCbSIKEBMzvOZPqN0ymerzhdpnTh7BFn89ri1zh85HDQ8UQiTkVIJJM5up7R3M5zmdJuCvEnx9Nxckcqv1CZ95a/xxE/EnREkYhRERLJpI6u9Lrg1gWMv3Y8OSwHbce1pcZLNfhw1Ye4a5UUiX0qQiKZnJnRumJrlnRdwhtXvcGeA3to8U4Lar9Sm8++/yzoeCLpoiIkEiPicsRxw7k3sKL7CkY1H8VPu3/istcvo9/afqz6Y1XQ8UROiIqQSIzJFZeLW2rcwuoeqxnWdBg//PkD9625j8e/f5wN+zYEHU8kTXIGHUBETszJOU+m5wU9OWPzGUzZPoWJ2yZy16q7qF+wPpV/q0y5QuWCjiiSIl0JicS4PHF5uKboNbxU6SVan9GaeTvmcfaIs+n2n25s2b0l6HgiycrIIvQDsDkDzy8iSeTLmY/2xdvzYqUX6VKjC6MWjaLc8HLc/+n9/L7v96DjiRxXhhUhd09w90YZdX4ROb5CuQoxotkIVnZfSeuKrRk0ZxBlh5flidlPsPfg3qDjifxFzN+OM7PRZrbNzJb9w/6GZrbTzBaHv/pHO6NIEMoVKscbrd9gcdfF1CtVjwc+e4Dyz5Zn5MKRmgpIMg2L9QfezOwiYA8w1t0rH2d/Q6CPu1+Z2nMmJib6kCFDIhdSJBNYvmc5r295nZV/rKR47uLcUOwG6hSog5kFHU2yiFatWi1095ppeU/MXwm5+yzgt6BziGR25+Q9h4GJA+lbpi85LSeDNwzm3jX3snT30qCjSTYW80UolWqb2bdmNs3MzjneAWbWxcwWmNmCXbu07LJkTWZGrQK1eKbCM/Q4swe/HfyNfuv68ci6R/SMkQQiOxShRUBpd68KPAtMOt5B7j7S3Wu6e838+fNHNaBItMVZHJeedinPV3yeDsU7sGrvKu5adRfDNg5j+4HtQceTbCTDi5CZBTr/vLvvcvc94e+nArnMrHCQmUQyi9w5cnPVGVfxYsUXaXl6S2bvmE23Fd0Y+9NY/jis5cYl40VjxoRAP/U0s6LAVnd3M6tFqPD+mtx74uPjadky7SuTT548+W/bTuQ8mUlW61NW6w9Erk83ciM/7PyBf33+L15f8jozd8+k30X9uP382zkp7qRIRE01/Zxiw/H6lFbRuB2XocPvzOxtYC5Qwcw2mVlnM+tqZl3Dh1wNLDOzb4HhwHUe60MCRTJIqQKlGHvVWBZ1WUS1otXo9XEvKo2oxPvL39fSEZIhUn0lZGZ5gAuBs4D48OYdwGpgnrvvi3y8lLl7uxT2Pwc8F6U4IllC9WLV+aT9J3y87mPu+eQerh13LbVL1mZI4yHUPrN20PEkC0nxSsjMCprZ88A24FPgeeDx8Nfz4W3bzGyEmRXMyLAiEj1mRtPEpiy+bTEvN3+Z9TvWU2d0HdqOa8v3v38fdDzJIpItQmYWD8wBjt7a+oRQ4RkY/no+vA3gdmCOmRXImKgiEoS4HHF0rtGZNT3W8FCDh5iyegoVR1Skz/Q+mpNO0i2lK6GHgLOBZ4Bi7t7U3Xu4+7/CXz3cvSlQDBgaPlbT4ohkQXlPysvDDR9m9R2rubHKjTw992nKP1ue5755TtMAyQlLqQi1Aj53995Hhzkfj7vvcfe7gRlA6wjmE5FMpkT+ErzS8hUW3baIc4ucS49pPTj3xXOZumYqExdtou4Tn1Pm/v9Q94nPmfRfTaQvyUupCBUDvknD+eaF3yMiWVy1otX47KbPmNR2EoeOHKLZW81oP7kl63euxIHNO/bxwISlKkSSrJSK0K9AhTScryLJPINjZo+n4VwiksmZGS3PbsnybstJiOvGPlvFltw9+C3XCxxmF/sOHmbwx6uCjimZWEpF6GOglZl1S+lEZnYH0AL46NhdSb6/PzzSTkSykJPiToI9V1D8z1HkO3w5u+Om8dPJXdgV9yGbd+wOOp5kYik9J9QPaAY8a2a9gemEngvaGd5fgNBzQ42BBELDuI8dmJD0CbexQNfwqLub3P3QsQ2aWV1gsLvXSVtXRCRIxePzsHkHFDp4O3kPXc7vuUbx+0kv8adNY/q6PDQu1zjoiJIJJVuE3H2zmdUGXgAaAbfx9xkQjl7pTAe6ufs/3gB2945m9itwF1DAzNq4+58AZlYeeBKI7XksRLKpe5pU4IEJS9l38DAneQJnHHiUwyfN53C+12jyRhNaVGjB042fplyhckFHlUwkxRkT3P17oImZlQUuJvQZ0dFngXYCq4AvwselyN17hwvRo8B0M7sFuBO4BcgFLAAeSGtHRCRYraqXAGDwx6v4acc+SsSfwj1NunB5lb4MnTeUAbMGUOn5SvSp3YcH6j9A3pPyBpxYMoNUT9sTLjIReUza3R83s52EllZYEd68GviXu4+PRBsiEn2tqpf4XzFK6r5699G+anvu+/Q+Hp/9OK99+xqDGg2iXeV2Wtk1m4v6ekIWchNw99FNwM9APRUgkayreL7ivH7V68y+eTZF8hbhhgk30PC1hizdqpVds7OoFiEzuwpYCrxK6HmiJ4DeQFHgUzM7I5p5RCT66paqyze3fMNLV77Esm3LqP5SdXp91Iudf+5M+c2S5US0CJnZYDNbd+zmJN+PJzS1z1jgLHfv6+7PAO2BSoTmnkuIZCYRyXzicsTR5bwurL5jNbfWuJXhXw+nwnMVGPvtWC0Zkc1E+kqoMKGh2kkl/Rf1CVDD3W92903/O8D9LeAqoDgw28zOiXAuEcmETjvlNF648gXm3zqfhPgEOkzqwEVjLmLDvg1BR5MoiertOHdv4u5L/mHfVKAJkBeYGc1cIhKs84qfx1edv+KVFq+wYvsK7l51N69ufpV9hwNZpkyiKNnRcWY2No3nS9cDpu4+28waAtPScx4RiT05LAedqneiZYWWtBvdjsnbJzN7x2w6l+hM7QJaSC+rSmmI9o2EbqelZQxlum7ouvtiM6uXnnOISOw67ZTT6H5mdy4rdBkvbnqRQRsGUT1fdar8VkUPumZBKRWh3cAmIMW548LuJzSFT7q4+7GDG0Qkm6lwagWeOusppv4ylbe2vEXlFyrT/6L+9K7TOzRXnWQJKRWhb4Gq7p6qz2jMrGO6E4mIhMVZHM1Pb07tArWZ6lPp+3lf3lz6Ji9d+RJ1S9UNOp5EQEoDExYDec1M18AiEpjCJxVm/LXj+eC6D9h9YDf1Xq1Hlw+7aHnxLCClIjQTWAKUTOX5JgGPpCuRiMg/aF6hOcu7Lad37d6M/u9oKo6oyLjvxunZohiWbBFy9/HuXj21t+PcfbK7/zsy0URE/i7vSXl5qvFTfHPrNxTPV5xr3r+GVu+2YtOuTSm/WTKdaDwnpNkJRSTiahSrwTe3fsPgRoP5ZN0nVBpRiRfmv8ARPxJ0NEmDEy5CZpYnNce5+z+2kdpziIgcT84cOelTpw/Lui3jgpIX0G1qNxqMacDqX1cHHU1SKT1XQuvN7E4zy53WN5pZVTObDPRJR/siIgCULViW6TdOZ0zLMSzbtoyqL1Zl8JzBHDryt8WbJZNJTxH6GHga2GJmL5jZxcld2ZhZWTO73czmAouAqsAX6WhfROR/zIwO1TrwXbfvaJrYlHs/vZc6r9Rh2bZlQUeTZJxwEXL3DsCFhFZC7QJ8Cuw0s2/N7CMze9vMJprZLDPbCqwBRgBlgAeBCu4+O/1dEBH5f8XyFWPCtRN49+p32bBjAzVeqsGAmQM4ePhg0NHkONI1MMHd57t7Y0LLMwwm9HBrJUKzJrQFWgJHp+CZAFwPnOnuT7j7/vS0LSLyT8yMa8+5lu+6f8fVla6m/4z+XPjKhboqyoQiMjrO3de4+/3ufj5QAKhAaDLT6kAJdy/i7te4+zvurj9HRCQqCp9SmLfavMWEayfw484fOW/keQz8cqA+K8pEIj5E2933hovSPHf/1t23RLoNEZG0uKriVSzvtpwWFVrQ9/O+1Btdj5W/rAw6lhDl9YRERIJy+qmn8/417/NOm3dY89saqr9UnWHzhum5ooCpCIlIttK2cluWd1vOZWUvo9fHvWj8emPNthAgFSERyXaK5i3KB9d9wKjmo5i3aR5VXqjC20vfDjpWtqQiJCLZkplxS41bWNx1MWcXPpvrJ1xPu/HtNDN3lMV8ETKz0Wa2zcyOO/bSQoab2VozW2JmNaKdUUQyr8RCiXx585c8evGjjPtuHOe+eC4zN6RqzmaJAIv1KdDN7CJgDzDW3SsfZ/8VQA/gCuACYJi7X5DcORMTE33IkCEZEVdEMrG1e9cyZMMQfj7wM1cXuZq2RduS01Ja+1OOatWq1UJ3r5mW90T8SsjMWprZ6H96HWnuPgv4LZlDWhIqUO7u84B4MyuWUXlEJHYlnpLI0xWe5pJCl/D+1vd5cM2DbN2/NehYWVpG3I6rBnRI5nW0lQB+TPJ6U3jbX5hZFzNbYGYLdu3aFbVwIpK55InLQ49SPehdujc//vkjd626i5m/6/ZcRon5z4Qixd1HuntNd6+ZP3/+oOOISMDqF6zPMxWeoVSeUjyz8Rme++E59h/RbGORlh2K0GbgzCSvS4a3iYgkq0juIjyW+BhXF7maT3/7lHtW38OmP/VMUSRlh0/cPgDuMLN3CA1M2JnSVELx8fG0bNkyzQ1Nnjz5b9tO5DyZSVbrU1brD6hP0dCa1ny09iPaT2zPfevu44VmL9C+avs0nSOz9SkSjtentIr5KyEzexuYC1Qws01m1tnMuppZ1/AhU4HvgbXAKKBbQFFFJIY1TWzK4tsWU6NYDW6adBOdJndi78G9QceKeTF/JeTu7VLY70D3KMURkSysRBbkRcMAABFxSURBVP4SfN7hcx6e8TCPf/k4C7csZMK1EyhXqFzQ0WJWzF8JiYhEU84cOXn0kkf5z/X/+d/yEFNWTwk6VsxSERIROQGXl7+chV0WUrZgWZq/3Zz+X/Tn8JHDQceKOSpCIiInqEzBMszpNIebq93MgFkDaPZWM37d+2vQsWKKipCISDrkyZWHV1q8wsgrR/LFhi+oOaomS7cuDTpWzFAREhFJJzPj1vNu5cubv+TA4QPUfqU2E1dMDDpWTMiIIrQT+CGZ1yIiWVKtErWYf+t8zjnjHFq/15pHZj6ilVtTEPEi5O5D3b3MP70WEcnKiucrzsyOM7mp6k08NOMhrn3/Wv448EfQsTIt3Y4TEYmwk3OezJiWYxjSeAgTV06k7ui6bD+wPehYmZKKkIhIBjAz7q59N/+5/j+s37Ge+9bcx/d7vw86VqajIiQikoGaJjZlTqc55CAHfdf2Zf7O+UFHylRUhEREMljlMyoz6KxBlMhdgoHrBzJ1+9SgI2UaKkIiIlFQKFchHkt8jJr5azJy80hGbx6tGRZQERIRiZqT407mvjL3cWXhK/lg+we0G9+O/Yey90J5MT+LtohILImzOG4peQuFTyrMmO/G8PufvzPh2gnky50v6GiBiNiVkJk1MrNBZjbPzH4yswNmttPM1pjZ+2Z2u5mViFR7IiKxrNUZrRjTcgxfrP+CS8deyi97fwk6UiDSVYTM7BQzu9/M1gMfAX2AWkA8sA04BJQF2gAjgPVmNt7MaqcvtohI7OtQrQMT205k6bal1Btdjx92Zr/JZU64CJlZJ2AN8DiwD/g30AiId/dT3L2ku59G6JZfJaATMB64HJhtZu+aWan0dkBEJJY1r9Cc6TdO5+c9P1N3dF2+2/5d0JGiKj1XQi8DXwMXuHsld3/E3T9z911JD/KQle4+JrwKalGgF1AP6JiO9kVEsoT6peszs+NMDh05RIMxDViydUnQkaImPUWopru3dvc0PXnl7rvc/VmgHPBeOtoXEckyqhatyqyOs8gdl5uLX7uYxT8vDjpSVJxwEXL3Relp2N3/dPeV6TmHiEhWUv608szsOJNTc53KJa9dwqIt6fo1GxMiOTru8UidS0QkuypXqBwzO84kf+78XDr2UuZvztrT/ETyYdX7zez5CJ5PRCRbKlOwDDM7zqTgyQW57PXLmLdpXtCRMkwki9BYoKuZvWVmx30I1szqmtlXEWxTRCRLKh1fmpkdZ3L6KafT+PXGLPxpYdCRMkTEipC7dwSeAa4DJpvZyUf3mVl5M5sAzAIuiFSbIiJZ2ZkFzmRGxxkUylOIpm82ZeUvWe9j9IjOHefuvYF/EXoWaLqZnWVmI4BlQCtgIdA4km2KiGRlJfOX5NObPiXO4mj0eiM27tgYdKSIyojlvR8HehB6DmgF0BX4HrjG3Wu5+2eRblNEJCtLLJTI9PbT2XNgD41eb8S2P7YFHSliIlqELOQm4O6jm4CfgXruPj6SbYmIZCfnFjmX/1z/Hzbt2kSTN5qw488dQUeKiEgO0b4KWAq8ChQDngB6E5oh4VMzOyNSbYmIZEd1zqzDxLYTWb5tOc3fbs7eg3uDjpRukbwSGg+cTWiU3Fnu3tfdnwHaE5o7bo6ZJUSwPRGRbKdJYhPebP0mc36YQ/uJ7TniR4KOlC6RLEKfADXc/WZ333R0o7u/BVwFFCc0cek5EWxTRCTbueacaxjSeAgTVkyg/xf9g46TLhFb1M7dmySzb6qZNQGmADOBwpFqV0QkO+p1YS++2/4dj335GBULV+SGc28IOtIJidry3u4+G2gIHIxWmyIiWZWZMaLZCBomNKTzB52Z++PcoCOdkPSsJ5Qnre9x98WEhm6f8DlERCTkpLiTGHfNOErmL0mrd1vF5DNE6bkSWm9md5pZ7rS8yd3XmVlVM5tMaCVWERE5QaedchpTrp/C/kP7af52c3bv3x10pDRJTxH6GHga2GJmL5jZxcld2ZhZWTO73czmAouAqsAX6WhfRESAswufzfvXvM9327/jpkk34e5BR0q19Kwn1AG4EFgAdAE+BXaa2bdm9pGZvW1mE81slpltJbQU+AigDPAgUCH8OVG6mFlTM1tlZmvN7P7j7O9oZtvNbHH465b0tikiktk0KteIQY0GMWnlJJ6fHzsLGlgkKqaZlQc6A5cC1YC4Yw7ZTmjy0vHAeHePyOAEM4sDVgONgE3AfKCdu3+X5JiOhFaBvSO1501MTPQhQ4ZEIqKISNS4O4+uf5Qlu5cw+KzBJORJiGr7rVq1WujuNdPynoiMjnP3Ne5+v7ufDxQAKgB1gOpACXcv4u7XuPs7kSpAYbWAte7+vbsfAN4BWkbw/CIiMcPM6FmqJ3nj8vLUhqf48/CfQUdKUUZMYLo3XJTmufu37r4l0m0kUQL4McnrTeFtx2pjZkvMbJyZnXm8E5lZFzNbYGYLdu3alRFZRUQyXIGcBehVuheb92/mlZ9eCTpOiqL2nFCAPgQS3P1cQrM6vHa8g9x9pLvXdPea+fPnj2pAEZFIqpqvKq3PaM0nv37CnB1zgo6TrFgvQpuBpFc2JcPb/sfdf3X3/eGXLwPnRSmbiEhg2hVrR4VTKjDihxFs3b816Dj/KGLT9hyPmcUDdYHfgbmeZBSEmZ0K9Hb3R9LRxHygvJmVIVR8rgOuPyZDsSS3BFsQWuMoWfHx8bRsmfaPliZPnvy3bSdynswkq/Upq/UH1KdYEUSfavxeg2ovVWPM7jHMunoWOXNE9lf+8fqUVhl2JRSeqHQFMBmYDcw3s9JJDskLPJSeNtz9EHAHoWeWVgDvuftyM3vEzFqED+tpZsvN7FugJ9AxPW2KiMSKMgXL8EKzF5i7aS4vLngx6DjHlZG34wYCcwmNlitBaHXVOeHh3BHj7lPd/Sx3L+fuj4W39Xf3D8LfP+Du57h7VXe/2N2z3iLtIiL/oF3ldlxW9jL6fdEvU67ImpFF6EKgn7v/4e5b3P1a4D1ghpmdlYHtiohImJkxvOlw9hzYwwOfPhB0nL/JyCKUG/jLk7DufjfhQgRUzMC2RUQkrOLpFbnrwrsYvXg08zbNCzrOX2RkEVoF/O3JWXe/C3if0GdFIiISBf0u6kfxfMXpPrU7h48cDjrO/2RkEZoItDveDne/E3gDsAxsX0REwvLlzseQxkNYtGURoxaNCjrO/2RYEXL3ge5+eTL7u7t7rD+nJCISM9qe05YGpRvw4OcP8uveX4OOA0SwCIVnz37VzHqYWd3wc0AiIpJJmBnPXfEcO//cSd/P+gYdB4jslVBZoAMwlNCM2TvNbIWZvWlmvcPrDRWIYHsiIpJGlc+oTM8LejJq0SgW/LQg6DgRLUIF+P/PeX4Evg1vawcMIrTe0K/hSULvMrNTIti2iIik0sMNHyb+5HgGzRkUdJSIFqH7gKuBS909wd3Pc/fihIZiv0aoOK0GEoAhwHIzOzeC7YuISCrkz52fTtU7MXHlRH7a/VOgWSJZhG4D3nH3vyzZ7e6r3L0T0AMoRGiNoQ5AYeBjMzs9ghlERCQVutbsyqEjhxi1MNiRcpEsQkWAf5yq1d1HAGuBe9z9deCq8HvuimAGERFJhcRCiTRNbMpLC1/i4OFIrjWaNpEsQt8TWt47ObMJzWSNu38aft08ghlERCSVup/fnS17tjBp5aTAMkSyCL0OnGdmyY37Kxr+OmoxUCaCGUREJJUuT7ychPgERswfEViGSBahZ4BvgAFmNt7MaiTdaWYXA23563LcByOcQUREUikuRxy317ydmRtnsnzb8kAyRKwAhFcvvRR4m9DnPfPNbJuZLTSz7wkN0c5N6Dmio8oBmeOxXRGRbKhT9U7kjsvN8/OfD6T9iF6FuPted78RqAO8BRwhNBruTEKLzrUPD1AgPCquCfB1JDOIiEjqFT6lMG0rt2XskrHs2r8r6u1nyK0wd5/n7u3dvSiQB8jj7pXd/c0kh/0KnA9kjrkjRESyqe7nd2fPgT28/u3rUW87wz+Pcff94WW4j91+xN2XufvqjM4gIiL/rFaJWtQsXpMR80fg7im/IYI0KEBEROh+fndW/LKCmRtnRrVdFSEREaHtOW0plKdQ1Idr54xqayIikinlyZWH3rV7s/fgXtwds+isOaoiJCIiAPStH/1xYrodJyIigVEREhGRwKgIiYhIYFSEREQkMCpCIiISGBUhEREJjIqQiIgERkVIREQCY9GerC4WmNl2YGM6TlEY+CVCcTKLrNanrNYfUJ9iRVbuU2l3Pz0tb1QRygBmtsDdawadI5KyWp+yWn9AfYoV6tNf6XaciIgERkVIREQCoyKUMUYGHSADZLU+ZbX+gPoUK9SnJPSZkIiIBEZXQiIiEhgVIRERCYyK0Akys9Fmts3Mlv3DfjOz4Wa21syWmFmNaGdMq1T06Wwzm2tm+82sT7TznYhU9OmG8M9nqZl9ZWZVo50xLVLRn5bh/iw2swVmVi/aGdMqpT4lOe58MztkZldHK9uJSsXPqaGZ7Qz/nBabWf9oZ0yr1Pycwv1abGbLzWxmas6rInTixgBNk9l/OVA+/NUFeCEKmdJrDMn36TegJ/BUVNJExhiS79N6oIG7VwEGkPk/NB5D8v35DKjq7tWATsDL0QiVTmNIvk+YWRzwJDA9GoEiYAwp9An40t2rhb8eiUKm9BpDMn0ys3jgeaCFu58DXJOak6oInSB3n0Xol/I/aQmM9ZB5QLyZFYtOuhOTUp/cfZu7zwcORi9V+qSiT1+5++/hl/OAklEJdoJS0Z89/v+jjU4FMv3Io1T8vwTQAxgPbMv4ROmXyj7FlFT06Xpggrv/ED4+VT8rFaGMUwL4McnrTeFtknl1BqYFHSK9zOwqM1sJ/IfQ1VBMM7MSwFXExt2EtKhtZt+a2TQzOyfoMBFwFlDQzGaY2UIzuyk1b8qZwaFEYoKZXUyoCGX6z1BS4u4TgYlmdhGhW4yXBRwpvYYC97n7ETMLOkukLCI0z9oeM7sCmETo1n0sywmcB1wK5AHmmtk8d1+d0pskY2wGzkzyumR4m2QyZnYuoc9OLnf3X4POEynuPsvMyppZYXeP5QkzawLvhAtQYeAKMzvk7pOCjXXi3H1Xku+nmtnzWeDntAn41d3/AP4ws1lAVSDZIqTbcRnnA+Cm8Ci5C4Gd7r4l6FDyV2ZWCpgAtE/pL7ZYYGaJFv5tHR6RmRuI6cLq7mXcPcHdE4BxQLdYLkAAZlY0yc+pFqHfxTH9cwImA/XMLKeZnQJcAKxI6U26EjpBZvY20BAobGabgIeAXADu/iIwFbgCWAvsBW4OJmnqpdQnMysKLADyA0fMrBdQKelfdZlNKn5O/YHTgOfDvxMOZeYZjlPRnzaE/vg5COwD2iYZqJAppaJPMScVfboauN3MDhH6OV0X6z8nd19hZh8BS4AjwMvunuywe9C0PSIiEiDdjhMRkcCoCImISGBUhEREJDAqQiIiEhgVIRERCYyKkIiIBEZFSEREAqMiJCIigVEREhGRwKgIiWRyZjbdzNzM2hyz3cxsTHjfE0HlE0kPTdsjksmFlxxfBKwCqrj74fD2IcDdwEh3vy3AiCInTFdCIpmcu38LvA5UBNoDmFlfQgXoPeD24NKJpI+uhERigJmdSWhdlp+BIcCzwMdAC3c/EGQ2kfRQERKJEWY2ELg//PIroJG77w0wkki66XacSOzYnuT7zipAkhWoCInEADO7HniK0O04gDsDjCMSMSpCIpmcmV0BjAGWAecSGiV3i5lVCDKXSCSoCIlkYmZWDxgHbAKauPt24F9ATuDJILOJRIIGJohkUmZWDZgB7APqufu6JPvmAzWBi9z9y2ASiqSfroREMiEzSwQ+ApzQFdC6Yw55IPzfwVENJhJhuhISEZHA6EpIREQCoyIkIiKBURESEZHAqAiJiEhgVIRERCQwKkIiIhIYFSEREQmMipCIiARGRUhERALzf0sZXYBdXZuMAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "# 100 linearly spaced numbers\n",
        "x = np.linspace(1,2,100)\n",
        "p=1.365230013\n",
        "\n",
        "# plot the function\n",
        "plt.plot(p,p, '-o',linewidth=5)\n",
        "plt.ylabel('$g_3(x)=\\dfrac{1}{2}(10-x^3)^{1/2}$',fontsize=20)\n",
        "plt.xlabel('$x$',fontsize=20)\n",
        "plt.plot(x,0.5*(10-x**3)**0.5, 'b')\n",
        "plt.grid(True,linewidth=5)\n",
        "\n",
        "# show the plot\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "ojbj7TZlUQcD",
        "outputId": "6984c5f9-54c0-4e8f-8ac2-c903054ed383",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 288
        }
      },
      "execution_count": 58,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "# 100 linearly spaced numbers\n",
        "x = np.linspace(1,2,100)\n",
        "\n",
        "# plot the function\n",
        "p=1.365230013\n",
        "plt.plot(p,p, '-o',linewidth=5)\n",
        "plt.ylabel('$g_4(x)=(\\dfrac{10}{4+x})^{1/2}$',fontsize=20)\n",
        "plt.xlabel('$x$',fontsize=20)\n",
        "plt.plot(x,(10/(4+x))**0.5, 'y')\n",
        "plt.grid(True,linewidth=5)\n",
        "\n",
        "# show the plot\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "wQyzll44UW4N",
        "outputId": "5cf75aa6-5ec8-43a0-a593-e2cc12582e2d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 292
        }
      },
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "# 100 linearly spaced numbers\n",
        "x = np.linspace(1,2,100)\n",
        "\n",
        "# plot the function\n",
        "p=1.365230013\n",
        "plt.plot(p,p, '-o',linewidth=5)\n",
        "plt.ylabel('$g_5(x)=x-\\dfrac{x^3+4x^2-10}{3x^2+8x}$',fontsize=20)\n",
        "plt.xlabel('$x$',fontsize=20)\n",
        "plt.plot(x,x-((x**3+4*x**2-10)/(3*x**2+8*x)), 'black')\n",
        "plt.grid(True,linewidth=5)\n",
        "\n",
        "# show the plot\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "fZrAiYAOUa3J",
        "outputId": "dd98422f-3c0a-4c2f-d537-df00fb3f0cb2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 302
        }
      },
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def abs(x):\n",
        "   if x >= 0:\n",
        "      return x\n",
        "   return -x \n",
        "\n",
        "def absolute_error(p, p0):\n",
        "  return abs(p-p0)\n",
        "\n",
        "# It returns a string to show more digits.\n",
        "def fixed_point_iteration(g,p0,N, TOL=5*10**-5):\n",
        "  if N == 0:\n",
        "    return str(p0)\n",
        "  for i in range(N):\n",
        "    try:\n",
        "      p = g(p0)\n",
        "      if isinstance(p, complex):\n",
        "         return \"\"\n",
        "      p0 = p\n",
        "    except OverflowError:\n",
        "      return \"\"\n",
        "  return str(p)"
      ],
      "metadata": {
        "id": "Swl8VKi4dVQo"
      },
      "execution_count": 51,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "import warnings\n",
        "warnings.filterwarnings(\"ignore\")\n",
        "\n",
        "n=np.arange(0, 30)\n",
        "p0=1.1\n",
        "\n",
        "def g1(n):\n",
        "  return fixed_point_iteration(lambda x: x-x**3-4*x**2+10, p0, n)\n",
        "\n",
        "def g2(n):\n",
        "  return fixed_point_iteration(lambda x: (10/x-4*x)**0.5, p0, n)\n",
        "\n",
        "def g3(n):\n",
        "  return fixed_point_iteration(lambda x: 0.5*(10-x**3)**0.5, p0, n)\n",
        "\n",
        "def g4(n):\n",
        "  return fixed_point_iteration(lambda x: (10/(4+x))**0.5, p0, n)\n",
        "\n",
        "def g5(n):\n",
        "  return fixed_point_iteration(lambda x: x-((x**3+4*x**2-10)/(3*x**2+8*x)), p0, n)\n",
        "\n",
        "\n",
        "data, indices = ([\n",
        "                  np.vectorize(g1)(n),\n",
        "                  np.vectorize(g2)(n),\n",
        "                  np.vectorize(g3)(n),\n",
        "                  np.vectorize(g4)(n),\n",
        "                  np.vectorize(g5)(n)], \n",
        "                 [\n",
        "                  \"g1\", \n",
        "                  \"g2\", \n",
        "                  \"g3\", \n",
        "                  \"g4\", \n",
        "                  \"g5\"\n",
        "                  ])\n",
        "\n",
        "df=pd.DataFrame(data,indices)\n",
        "df.T"
      ],
      "metadata": {
        "id": "u5-VuZYkZKbI",
        "outputId": "1d5349a1-2e3b-4667-c6c5-3ad24b592e8b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 656
        }
      },
      "execution_count": 61,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-3bf427ec-08b9-46d1-9c6f-47b8fdbc8b1f\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>g1</th>\n",
              "      <th>g2</th>\n",
              "      <th>g3</th>\n",
              "      <th>g4</th>\n",
              "      <th>g5</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1.1</td>\n",
              "      <td>1.1</td>\n",
              "      <td>1.1</td>\n",
              "      <td>1.1</td>\n",
              "      <td>1.1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>4.9289999999999985</td>\n",
              "      <td>2.165850662190053</td>\n",
              "      <td>1.472158279533828</td>\n",
              "      <td>1.4002800840280099</td>\n",
              "      <td>1.4080450522928398</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>-202.00142108899982</td>\n",
              "      <td></td>\n",
              "      <td>1.3047475779514128</td>\n",
              "      <td>1.3607923449481314</td>\n",
              "      <td>1.366101340826865</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>8079171.661661471</td>\n",
              "      <td></td>\n",
              "      <td>1.39452875272817</td>\n",
              "      <td>1.3657949658048225</td>\n",
              "      <td>1.3652303853796224</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-5.2735215203930925e+20</td>\n",
              "      <td></td>\n",
              "      <td>1.3498190038521356</td>\n",
              "      <td>1.3651581405352602</td>\n",
              "      <td>1.3652300134141646</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>1.4665678760633066e+62</td>\n",
              "      <td></td>\n",
              "      <td>1.3730089642613386</td>\n",
              "      <td>1.3652391578493726</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>-3.1543254772104814e+186</td>\n",
              "      <td></td>\n",
              "      <td>1.3612188643181122</td>\n",
              "      <td>1.3652288499745515</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3672760056485993</td>\n",
              "      <td>1.3652301614378386</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3641805707465915</td>\n",
              "      <td>1.365229994581125</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.365766768990587</td>\n",
              "      <td>1.3652300158102046</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3649550796179333</td>\n",
              "      <td>1.3652300131092414</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3653707332693255</td>\n",
              "      <td>1.3652300134528834</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3651579609730242</td>\n",
              "      <td>1.365230013409162</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3652668990271724</td>\n",
              "      <td>1.3652300134147246</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3652111287685122</td>\n",
              "      <td>1.365230013414017</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3652396814529828</td>\n",
              "      <td>1.365230013414107</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3652250637087506</td>\n",
              "      <td>1.3652300134140956</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3652325474599187</td>\n",
              "      <td>1.365230013414097</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3652287160777932</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3652306775992262</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3652296733768365</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3652301874999448</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>22</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3652299242888732</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3652300590427544</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>24</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.365229990053991</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3652300253735656</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>26</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3652300072913122</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>27</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3652300165487254</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>28</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3652300118092884</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>29</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3652300142356966</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
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            ],
            "text/plain": [
              "                          g1                 g2                  g3  \\\n",
              "0                        1.1                1.1                 1.1   \n",
              "1         4.9289999999999985  2.165850662190053   1.472158279533828   \n",
              "2        -202.00142108899982                     1.3047475779514128   \n",
              "3          8079171.661661471                       1.39452875272817   \n",
              "4    -5.2735215203930925e+20                     1.3498190038521356   \n",
              "5     1.4665678760633066e+62                     1.3730089642613386   \n",
              "6   -3.1543254772104814e+186                     1.3612188643181122   \n",
              "7                                                1.3672760056485993   \n",
              "8                                                1.3641805707465915   \n",
              "9                                                 1.365766768990587   \n",
              "10                                               1.3649550796179333   \n",
              "11                                               1.3653707332693255   \n",
              "12                                               1.3651579609730242   \n",
              "13                                               1.3652668990271724   \n",
              "14                                               1.3652111287685122   \n",
              "15                                               1.3652396814529828   \n",
              "16                                               1.3652250637087506   \n",
              "17                                               1.3652325474599187   \n",
              "18                                               1.3652287160777932   \n",
              "19                                               1.3652306775992262   \n",
              "20                                               1.3652296733768365   \n",
              "21                                               1.3652301874999448   \n",
              "22                                               1.3652299242888732   \n",
              "23                                               1.3652300590427544   \n",
              "24                                                1.365229990053991   \n",
              "25                                               1.3652300253735656   \n",
              "26                                               1.3652300072913122   \n",
              "27                                               1.3652300165487254   \n",
              "28                                               1.3652300118092884   \n",
              "29                                               1.3652300142356966   \n",
              "\n",
              "                    g4                  g5  \n",
              "0                  1.1                 1.1  \n",
              "1   1.4002800840280099  1.4080450522928398  \n",
              "2   1.3607923449481314   1.366101340826865  \n",
              "3   1.3657949658048225  1.3652303853796224  \n",
              "4   1.3651581405352602  1.3652300134141646  \n",
              "5   1.3652391578493726  1.3652300134140969  \n",
              "6   1.3652288499745515  1.3652300134140969  \n",
              "7   1.3652301614378386  1.3652300134140969  \n",
              "8    1.365229994581125  1.3652300134140969  \n",
              "9   1.3652300158102046  1.3652300134140969  \n",
              "10  1.3652300131092414  1.3652300134140969  \n",
              "11  1.3652300134528834  1.3652300134140969  \n",
              "12   1.365230013409162  1.3652300134140969  \n",
              "13  1.3652300134147246  1.3652300134140969  \n",
              "14   1.365230013414017  1.3652300134140969  \n",
              "15   1.365230013414107  1.3652300134140969  \n",
              "16  1.3652300134140956  1.3652300134140969  \n",
              "17   1.365230013414097  1.3652300134140969  \n",
              "18  1.3652300134140969  1.3652300134140969  \n",
              "19  1.3652300134140969  1.3652300134140969  \n",
              "20  1.3652300134140969  1.3652300134140969  \n",
              "21  1.3652300134140969  1.3652300134140969  \n",
              "22  1.3652300134140969  1.3652300134140969  \n",
              "23  1.3652300134140969  1.3652300134140969  \n",
              "24  1.3652300134140969  1.3652300134140969  \n",
              "25  1.3652300134140969  1.3652300134140969  \n",
              "26  1.3652300134140969  1.3652300134140969  \n",
              "27  1.3652300134140969  1.3652300134140969  \n",
              "28  1.3652300134140969  1.3652300134140969  \n",
              "29  1.3652300134140969  1.3652300134140969  "
            ]
          },
          "metadata": {},
          "execution_count": 61
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "import warnings\n",
        "warnings.filterwarnings(\"ignore\")\n",
        "\n",
        "n=np.arange(0, 30)\n",
        "p0=1.3\n",
        "\n",
        "def g1(n):\n",
        "  return fixed_point_iteration(lambda x: x-x**3-4*x**2+10, p0, n)\n",
        "\n",
        "def g2(n):\n",
        "  return fixed_point_iteration(lambda x: (10/x-4*x)**0.5, p0, n)\n",
        "\n",
        "def g3(n):\n",
        "  return fixed_point_iteration(lambda x: 0.5*(10-x**3)**0.5, p0, n)\n",
        "\n",
        "def g4(n):\n",
        "  return fixed_point_iteration(lambda x: (10/(4+x))**0.5, p0, n)\n",
        "\n",
        "def g5(n):\n",
        "  return fixed_point_iteration(lambda x: x-((x**3+4*x**2-10)/(3*x**2+8*x)), p0, n)\n",
        "\n",
        "\n",
        "data, indices = ([\n",
        "                  np.vectorize(g1)(n),\n",
        "                  np.vectorize(g2)(n),\n",
        "                  np.vectorize(g3)(n),\n",
        "                  np.vectorize(g4)(n),\n",
        "                  np.vectorize(g5)(n)], \n",
        "                 [\n",
        "                  \"g1\", \n",
        "                  \"g2\", \n",
        "                  \"g3\", \n",
        "                  \"g4\", \n",
        "                  \"g5\"\n",
        "                  ])\n",
        "\n",
        "df=pd.DataFrame(data,indices)\n",
        "df.T"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 990
        },
        "id": "dU8yPgTg_9PA",
        "outputId": "75257356-17de-4000-b5ec-2daf8e1527ad"
      },
      "execution_count": 62,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-0751d1bd-0256-46bf-b58d-7ee97457d08c\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>g1</th>\n",
              "      <th>g2</th>\n",
              "      <th>g3</th>\n",
              "      <th>g4</th>\n",
              "      <th>g5</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1.3</td>\n",
              "      <td>1.3</td>\n",
              "      <td>1.3</td>\n",
              "      <td>1.3</td>\n",
              "      <td>1.3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2.342999999999999</td>\n",
              "      <td>1.5787044347526522</td>\n",
              "      <td>1.3966925216381736</td>\n",
              "      <td>1.3736056394868903</td>\n",
              "      <td>1.367420814479638</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>-22.47784360699997</td>\n",
              "      <td>0.1396072283473371</td>\n",
              "      <td>1.3486476618648708</td>\n",
              "      <td>1.3641656335521124</td>\n",
              "      <td>1.3652323626465632</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>9323.516446902682</td>\n",
              "      <td>8.430367726506821</td>\n",
              "      <td>1.3735912332743274</td>\n",
              "      <td>1.36536545397988</td>\n",
              "      <td>1.3652300134168025</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-810821957334.5781</td>\n",
              "      <td></td>\n",
              "      <td>1.3609163080435307</td>\n",
              "      <td>1.3652127817181416</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>5.3306050091602565e+35</td>\n",
              "      <td></td>\n",
              "      <td>1.3674297206353376</td>\n",
              "      <td>1.3652322057977513</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>-1.5147100578733688e+107</td>\n",
              "      <td></td>\n",
              "      <td>1.364101566687551</td>\n",
              "      <td>1.365229734478521</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3658071350431369</td>\n",
              "      <td>1.3652300489029048</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.364934392575762</td>\n",
              "      <td>1.365230008898877</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3653813186755845</td>\n",
              "      <td>1.3652300139885656</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3651525401990343</td>\n",
              "      <td>1.3652300133410076</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3652696738716912</td>\n",
              "      <td>1.365230013423396</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.365209708055586</td>\n",
              "      <td>1.3652300134129138</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3652404087767323</td>\n",
              "      <td>1.3652300134142474</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3652246913402981</td>\n",
              "      <td>1.3652300134140776</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3652327380963376</td>\n",
              "      <td>1.3652300134140993</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3652286184788607</td>\n",
              "      <td>1.3652300134140964</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3652307275659745</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.365229647795765</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3652302005964538</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.365229917583966</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3652300624754066</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>22</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3652299882966061</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3652300262732786</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>24</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.365230006830694</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.365230016784544</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>26</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3652300116885585</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>27</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3652300142975056</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>28</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3652300129618258</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>29</th>\n",
              "      <td></td>\n",
              "      <td></td>\n",
              "      <td>1.3652300136456421</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "      <td>1.3652300134140969</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
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              "              title=\"Convert this dataframe to an interactive table.\"\n",
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              "    .colab-df-convert {\n",
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              "          const element = document.querySelector('#df-0751d1bd-0256-46bf-b58d-7ee97457d08c');\n",
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              "                                                     [key], {});\n",
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              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
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            "text/plain": [
              "                          g1                  g2                  g3  \\\n",
              "0                        1.3                 1.3                 1.3   \n",
              "1          2.342999999999999  1.5787044347526522  1.3966925216381736   \n",
              "2         -22.47784360699997  0.1396072283473371  1.3486476618648708   \n",
              "3          9323.516446902682   8.430367726506821  1.3735912332743274   \n",
              "4         -810821957334.5781                      1.3609163080435307   \n",
              "5     5.3306050091602565e+35                      1.3674297206353376   \n",
              "6   -1.5147100578733688e+107                       1.364101566687551   \n",
              "7                                                 1.3658071350431369   \n",
              "8                                                  1.364934392575762   \n",
              "9                                                 1.3653813186755845   \n",
              "10                                                1.3651525401990343   \n",
              "11                                                1.3652696738716912   \n",
              "12                                                 1.365209708055586   \n",
              "13                                                1.3652404087767323   \n",
              "14                                                1.3652246913402981   \n",
              "15                                                1.3652327380963376   \n",
              "16                                                1.3652286184788607   \n",
              "17                                                1.3652307275659745   \n",
              "18                                                 1.365229647795765   \n",
              "19                                                1.3652302005964538   \n",
              "20                                                 1.365229917583966   \n",
              "21                                                1.3652300624754066   \n",
              "22                                                1.3652299882966061   \n",
              "23                                                1.3652300262732786   \n",
              "24                                                 1.365230006830694   \n",
              "25                                                 1.365230016784544   \n",
              "26                                                1.3652300116885585   \n",
              "27                                                1.3652300142975056   \n",
              "28                                                1.3652300129618258   \n",
              "29                                                1.3652300136456421   \n",
              "\n",
              "                    g4                  g5  \n",
              "0                  1.3                 1.3  \n",
              "1   1.3736056394868903   1.367420814479638  \n",
              "2   1.3641656335521124  1.3652323626465632  \n",
              "3     1.36536545397988  1.3652300134168025  \n",
              "4   1.3652127817181416  1.3652300134140969  \n",
              "5   1.3652322057977513  1.3652300134140969  \n",
              "6    1.365229734478521  1.3652300134140969  \n",
              "7   1.3652300489029048  1.3652300134140969  \n",
              "8    1.365230008898877  1.3652300134140969  \n",
              "9   1.3652300139885656  1.3652300134140969  \n",
              "10  1.3652300133410076  1.3652300134140969  \n",
              "11   1.365230013423396  1.3652300134140969  \n",
              "12  1.3652300134129138  1.3652300134140969  \n",
              "13  1.3652300134142474  1.3652300134140969  \n",
              "14  1.3652300134140776  1.3652300134140969  \n",
              "15  1.3652300134140993  1.3652300134140969  \n",
              "16  1.3652300134140964  1.3652300134140969  \n",
              "17  1.3652300134140969  1.3652300134140969  \n",
              "18  1.3652300134140969  1.3652300134140969  \n",
              "19  1.3652300134140969  1.3652300134140969  \n",
              "20  1.3652300134140969  1.3652300134140969  \n",
              "21  1.3652300134140969  1.3652300134140969  \n",
              "22  1.3652300134140969  1.3652300134140969  \n",
              "23  1.3652300134140969  1.3652300134140969  \n",
              "24  1.3652300134140969  1.3652300134140969  \n",
              "25  1.3652300134140969  1.3652300134140969  \n",
              "26  1.3652300134140969  1.3652300134140969  \n",
              "27  1.3652300134140969  1.3652300134140969  \n",
              "28  1.3652300134140969  1.3652300134140969  \n",
              "29  1.3652300134140969  1.3652300134140969  "
            ]
          },
          "metadata": {},
          "execution_count": 62
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "| Function |  Advantages |   Drawbacks |\n",
        "| ----------- | ----------- | ----------- |\n",
        "| g1(x) | No apply |  Function diverges |\n",
        "| g2(x) | No apply   |   It involved complex numbers after 3 iterations.      |\n",
        "| g3(x) | It converges to solution.   | But it converges on 30 iterations.        |\n",
        "| g4(x) | It converges to solution.    | But it converges on 15 iterations.      |\n",
        "| g5(x) | It converges to the solution fastest on 4 iterations.   | No apply        |\n"
      ],
      "metadata": {
        "id": "x_BNW6a8uNPF"
      }
    }
  ]
}