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@tobydriscoll
Created February 3, 2017 19:01
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Lecture 35: GMRES\n",
"\n",
"GMRES is simply the replacement of the problem \"solve $b-Ax=0$ with \"minimize $\\|b-Ax\\|$ over $\\mathcal{K}_n$\". Its convergence depends strongly on (at least) the spectrum of $A$.\n",
"\n",
"This example is adapted from the text."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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osFJw1ZuB08yMyepSyixV6VskaiIJLvBlwnNUZ3b5qKhfo5gytUrGWiVqxZQJ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8zUtKhsIkl+QaNcF3NIRiSIKrTGHaevonCLYBUUkBABS6IgDFbrVRYkdVfn4Xf2JEbzUmJ55Q8L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\nThvHEwREAAAAAElFTkSuQmCC\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"m = 1200;\n",
"A = 2*eye(m) + 0.5*randn(m,m)/sqrt(m);\n",
"plot(eig(A),'.')\n",
"axis equal, title('Eigenvalues of A')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We're going to do a lazy GMRES here. First we run Arnoldi, then successively solve the approximate least squares problems using brute force. "
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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aTx8PZ3YvXefEHoiVTAA2T3iu4zk4cZRlJ6moqKi6urpx48aidtry6NEjYaNS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\nkAAAgAv/H4SCcVszg0zyAAAAAElFTkSuQmCC\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"b = ones(m,1);\n",
"[Q,H] = arnoldi(A,b,15);\n",
"resnorm = [];\n",
"for n = 1:15\n",
" e1 = eye(n+1,1);\n",
" yn = H(1:n+1,1:n) \\ (norm(b)*e1);\n",
" resnorm(n) = norm( H(1:n+1,1:n)*yn - norm(b)*e1 );\n",
" xn = Q(:,1:n)*yn;\n",
"end\n",
"\n",
"semilogy(resnorm,'o-')\n",
"xlabel('n'), ylabel('norm of residual')\n",
"title('Convergence of GMRES residual')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The text explains why this might be very close to $4^{-n}\\|b\\|$. "
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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et29fI/0ZBsBbAjwnNpg7UYkQ0tW368vvfcwb0SAplUWnXkH3HQA0RyYOSLdu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\nAABJRU5ErkJggg==\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"semilogy(resnorm,'o-')\n",
"hold on\n",
"semilogy([1 15],norm(b)*.25.^([1 15]),'--')\n",
"xlabel('n'), ylabel('norm of residual')\n",
"title('Convergence of GMRES residual')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The rate is tied to how easy it is to make a polynomial small on the spectrum of $A$ while satisfying the normalization $p(0)=1$. If the set gets close to or surrounds the origin, this becomes difficult."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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W7DN7TSJmguXLl8/2FujY29Lxxh703MnjjT34R2lDJ3ruZPbhy7TD0HMn0XMnL964NZpa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VdEhIIhZ8y4YzSB0VuaoAqR4ctOqeQBQeYQ+jswwAkgg7Rr1y6X657641dffVUiud9M9dxqrasH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\nzXSCk2AAAAAASUVORK5CYII=\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"theta = linspace(0,pi,m)';\n",
"d = (-2+2*sin(theta)) + 1i*cos(theta);\n",
"D = diag(d);\n",
"A = A + D;\n",
"lam = eig(A);\n",
"plot(lam,'.')\n",
"axis equal, title('Eigenvalues of A')"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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0SMPnW8gtAGhrWkcgVVRUTJ48ec6cOYGBgYpLExMT4+PjHz16xOPxnJ2dg4OD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\nECey8PGPRQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"b = ones(m,1);\n",
"[Q,H] = arnoldi(A,b,80);\n",
"resnorm = [];\n",
"for n = 1:80\n",
" e1 = eye(n+1,1);\n",
" yn = H(1:n+1,1:n) \\ (norm(b)*e1);\n",
" resnorm(n) = norm( H(1:n+1,1:n)*yn - norm(b)*e1 );\n",
" xn = Q(:,1:n)*yn;\n",
"end\n",
"\n",
"semilogy(resnorm,'.-')\n",
"hold on, semilogy([0 80],norm(b)*.25.^([0 80]),'--')\n",
"xlabel('n'), ylabel('norm of residual')\n",
"title('Convergence of GMRES residual')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There is again a linear convergence rate (mainly because the matrix is close to normal and its spectrum uniformly covers the set), but a much slower one this time due to the shape of the spectrum."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"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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