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Trefethen & Bau lecture notes in MATLAB
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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": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans =\n",
"\n",
" 2.199999983865907 + 0.000000000000000i\n",
" 1.000139183421948 + 0.000225276870781i\n",
" 1.000139183421948 - 0.000225276870781i\n",
" 0.999721641527813 + 0.000000000000000i\n",
" 0.400000002917564 + 0.000000000000000i\n"
]
}
],
"source": [
" p = poly([1,1,1,0.4,2.2]); % polynomial with these as roots\n",
" q = p + 1e-9*randn(size(p)); % small changes to its coefficients\n",
" format long, 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, while the other two roots changed by an amount close to $10^{-9}$. The effect can be more dramatically shown using the Wilkinson polynomial. "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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Q7qjBkxRKWVQoXDr0sv+gkP8PFEjIv11a+d6ydu2lsupw9l2ZZXo12eW8pGfI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\nBUxICCGE9AImJIQQQnoBExJCCCG98H+HrYvAOSFvUgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"p = poly(1:20);\n",
"plot(1:20,0,'ko'), hold on\n",
"for k = 1:500\n",
" q = p.*(1+1e-9*randn(size(p))); % relative perturbations\n",
" r = roots(q);\n",
" plot(real(r),imag(r),'.')\n",
"end"
]
},
{
"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": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans =\n",
"\n",
" 20.000025067150030\n",
" 18.999711616114300\n",
" 18.001325588115538\n",
" 16.996775933863130\n",
" 16.004118811901026\n",
" 14.998789417426167\n",
" 13.994662465567782\n",
" 13.011037500812872\n",
" 11.987895363460201\n",
" 11.008916691876841\n",
" 9.995371923454529\n",
" 9.001777036204514\n",
" 7.999506222071467\n",
" 7.000098926981961\n",
" 5.999986252392936\n",
" 5.000001246518829\n",
" 3.999999934630949\n",
" 3.000000001450744\n",
" 2.000000000006418\n",
" 0.999999999999694\n"
]
}
],
"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": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"kappa =\n",
"\n",
" 4.7661e+05\n"
]
}
],
"source": [
"format short e\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": [
"bound =\n",
"\n",
" 4.7661e-05\n",
"\n",
" relative error = 6.83e-07\n",
" relative error = 7.47e-08\n",
" relative error = 6.05e-06\n",
" relative error = 8.56e-06\n",
" relative error = 1.31e-06\n",
" relative error = 4.15e-06\n",
" relative error = 1.23e-07\n",
" relative error = 4.04e-06\n"
]
}
],
"source": [
"perturb = @(z,ep) z.*(1 + ep*(2*rand(size(z))-1));\n",
"x = 0.3+(1:5)'; b = A*x;\n",
"bound = 1e-10*kappa\n",
"for k = 1:8\n",
" bb = perturb(b,1e-10);\n",
" fprintf(' relative error = %.2e\\n', norm( A\\bb - x ) / norm( x ) )\n",
"end"
]
},
{
"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": [
"bound =\n",
"\n",
" 4.7661e-05\n",
"\n",
" relative error = 5.39e-07\n",
" relative error = 1.03e-06\n",
" relative error = 2.32e-06\n",
" relative error = 1.99e-07\n",
" relative error = 5.80e-06\n",
" relative error = 2.40e-08\n",
" relative error = 7.13e-07\n",
" relative error = 6.53e-07\n"
]
}
],
"source": [
"x = 0.3+(1:5)'; b = A*x;\n",
"bound = 1e-10*kappa\n",
"for k = 1:8\n",
" AA = perturb(A,1e-10);\n",
" fprintf(' relative error = %.2e\\n', norm( AA\\b - x ) / norm( x ) )\n",
"end"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Matlab",
"language": "matlab",
"name": "matlab"
},
"language_info": {
"codemirror_mode": "octave",
"file_extension": ".m",
"help_links": [
{
"text": "MetaKernel Magics",
"url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
}
],
"mimetype": "text/x-octave",
"name": "matlab",
"version": "0.11.0"
}
},
"nbformat": 4,
"nbformat_minor": 1
}
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