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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": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x3213ac090>)"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"using PyPlot\n",
"\n",
"m = 1200;\n",
"A = 2*eye(m) + 0.5*randn(m,m)/sqrt(m);\n",
"lam = eigvals(A);\n",
"plot(real(lam),imag(lam),\".\");\n",
"axis(\"equal\");\n",
"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": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x32b4f6590>)"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"WARNING: Method definition arnoldi(Any, Any, Any) in module Main at /Users/driscoll/Dropbox/class/612/tbnotes/julia/Krylov.jl:3 overwritten at /Users/driscoll/Dropbox/class/612/tbnotes/julia/Krylov.jl:3.\n",
"WARNING: Method definition lanczos(Any, Any, Any) in module Main at /Users/driscoll/Dropbox/class/612/tbnotes/julia/Krylov.jl:22 overwritten at /Users/driscoll/Dropbox/class/612/tbnotes/julia/Krylov.jl:22.\n"
]
}
],
"source": [
"include(\"Krylov.jl\")\n",
"b = ones(m,1);\n",
"(Q,H) = arnoldi(A,b,15);\n",
"resnorm = [];\n",
"for n = 1:15\n",
" e1 = [1;zeros(n)];\n",
" yn = H[1:n+1,1:n] \\ (norm(b)*e1);\n",
" resnorm = [resnorm; 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": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x3213ebb10>)"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"semilogy(resnorm,\"o-\");\n",
"i = collect(1:15);\n",
"semilogy(i,norm(b)*.25.^i,\"r--\");\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": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x32afedd10>)"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"theta = linspace(0,pi,m);\n",
"d = (-2+2*sin(theta)) + 1im*cos(theta);\n",
"D = diagm(d);\n",
"A = A + D;\n",
"lam = eigvals(A);\n",
"plot(real(lam),imag(lam),\".\");\n",
"axis(\"equal\") \n",
"title(\"Eigenvalues of A\");"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x109cac950>)"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"1-element Array{Any,1}:\n",
" PyObject <matplotlib.lines.Line2D object at 0x109e366d0>"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"b = ones(m,1);\n",
"(Q,H) = arnoldi(A,b,80);\n",
"resnorm = [];\n",
"for n = 1:80\n",
" e1 = [1;zeros(n)];\n",
" yn = H[1:n+1,1:n] \\ (norm(b)*e1);\n",
" resnorm = [resnorm; 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\");\n",
"semilogy([0,80],norm(b)*.25.^([0,80]),\"r--\")\n"
]
},
{
"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."
]
}
],
"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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