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TB Lecture 12: Condition numbers
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Lecture 12: Condition numbers\n",
"\n",
"In numerical computing, as we will soon see, we constantly make small errors in representing real numbers and the operations on them. Consequently we need to know whether the problems we want to solve are very sensitive to perturbations. The condition number measures this senstivity.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Polynomial roots\n",
"\n",
"The roots of a polynomial become sensitive to the values of the coefficients in the monomial basis when roots are relatively close to one another. Consider, for example,"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Complex{Float64}[0.4+0.0im,0.999199+0.00138567im,0.999199-0.00138567im,1.0016+0.0im,2.2+0.0im]\n"
]
}
],
"source": [
"using Polynomials \n",
"p = poly([1,1,1,0.4,2.2]); # polynomial with these as roots\n",
"q = p + Poly(1e-9*randn(6)); # small changes to its coefficients\n",
"println(roots(q))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Observe that the triple root at 1 changed a lot more than the size of the perturbation would suggest; the other two roots changed by an amount less than $10^{-9}$. The effect of bad conditioning can be more dramatically shown using the _Wilkinson polynomial_. "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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",
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x3206e0f50>)"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"(0.0,25.0,-8.0,8.0)"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"p = poly(1.0:20);\n",
"using PyPlot\n",
"plot(collect(1:20),zeros(20),\"ko\")\n",
"for k = 1:500\n",
" q = Poly(p.a.*(1+1e-9*randn(21))); # relative perturbations\n",
" r = roots(q);\n",
" plot(real(r),imag(r),\".\")\n",
"end\n",
"axis(\"equal\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Clearly, having roots close together is not the only way to get sensitivity in the roots. In fact we can't accurately compute the roots even without perturbation to the data:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"20-element Array{Complex{Float64},1}:\n",
" 1.0+0.0im \n",
" 2.0+0.0im \n",
" 3.0+0.0im \n",
" 4.0+0.0im \n",
" 5.0+0.0im \n",
" 6.00005+0.0im \n",
" 6.99956+0.0im \n",
" 8.00288+0.0im \n",
" 8.98674+0.0im \n",
" 10.0499+0.0im \n",
" 10.8862+0.0im \n",
" 12.3578+0.0im \n",
" 12.562+0.0im \n",
" 14.5189+0.213088im\n",
" 14.5189-0.213088im\n",
" 16.2068+0.0im \n",
" 16.8857+0.0im \n",
" 18.0301+0.0im \n",
" 18.9939+0.0im \n",
" 20.0005+0.0im "
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"roots(p)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Matrix condition number\n",
"\n",
"We have particular interest in the condition number of the problem \"given square matrix $A$ and vector $b$, find vector $x$ such that $Ax=b$.\" More simply: \"map $b$ to $A^{-1}b$.\" The relative condition number of this problem is bounded above by the *matrix condition number* $\\kappa(A)=\\|A\\|\\,\\|A^{-1}\\|$. Furthermore, in any particular case there exist perturbations to the data such that the upper bound is achieved. "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"1.5350438953292724e6"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"hilb(n) = [ 1.0/(i+j) for i=1:n, j=1:n];\n",
"A = hilb(5); kappa = cond(A)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The importance of _relative_ condition numbers is that they explain accuracy in dimensionless terms, i.e. significant digits. This condition number says we could \"lose\" up to 5 or so digits in the passage from data to result. So we make relative perturbations to $b$ and see the relative effect on the result."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" relative error = 3.81e-05\n",
" relative error = 3.68e-06\n",
" relative error = 2.67e-05\n",
" relative error = 3.67e-05\n",
" relative error = 2.04e-05\n",
" relative error = 2.90e-06\n",
" relative error = 1.24e-05\n",
" relative error = 4.15e-05\n",
"bound = 1.0e-10kappa = 0.00015350438953292724\n"
]
}
],
"source": [
"perturb(z,ep) = z.*(1 + ep*(2*rand(size(z))-1));\n",
"x = 0.3+(1:5); b = A*x;\n",
"for k = 1:8\n",
" bb = perturb(b,1e-10);\n",
" @printf(\" relative error = %.2e\\n\", norm( A\\bb - x ) / norm( x ) )\n",
"end\n",
"@show bound = 1e-10*kappa;"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The same holds for perturbations to $A$, though the error has higher-order terms that vanish only in the limit of infinitesimal perturbations."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" relative error = 3.09e-06\n",
" relative error = 1.19e-05\n",
" relative error = 1.63e-06\n",
" relative error = 6.30e-06\n",
" relative error = 1.50e-05\n",
" relative error = 1.52e-05\n",
" relative error = 4.63e-06\n",
" relative error = 1.88e-05\n",
"bound = 1.0e-10kappa = 0.00015350438953292724\n"
]
}
],
"source": [
"x = 0.3+(1:5); b = A*x;\n",
"for k = 1:8\n",
" AA = perturb(A,1e-10);\n",
" @printf(\" relative error = %.2e\\n\", norm( AA\\b - x ) / norm( x ) )\n",
"end\n",
"@show bound = 1e-10*kappa;"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 0.5.0",
"language": "julia",
"name": "julia-0.5"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "0.5.0"
}
},
"nbformat": 4,
"nbformat_minor": 1
}
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