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@tobydriscoll
Created February 3, 2017 19:02
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Lecture 36: Lanczos (and MINRES)\n",
"\n",
"When $A^*=A$, a number of things about iterative methods get better and faster. The most notable development is that the Hessenberg matrix $H_n$ is also hermitian and thus tridiagonal. Consequently the Arnoldi iteration's loop to fill in $H$ becomes a fixed length process, greatly speeding up the computation as the dimension of $\\mathcal{K}_n$ increases. The result is known as the _Lanczos iteration_.\n",
"\n",
"We can fully demonstrate the properties of Lanczos using only diagonal matrices."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans =\n",
"\n",
" 5.0978 2.7363 0 0 0\n",
" 2.7363 5.3926 2.2944 0 0\n",
" 0 2.2944 5.4278 2.3514 0\n",
" 0 0 2.3514 5.6650 2.1131\n",
" 0 0 0 2.1131 5.5528\n"
]
}
],
"source": [
"m = 400;\n",
"kappa = 10;\n",
"N = 60;\n",
"lam = linspace(1,kappa,m)';\n",
"A = diag(lam);\n",
"b = randn(m,1);\n",
"b = b/norm(b);\n",
"[Q,T] = lanczos(A,b,N);\n",
"T(1:5,1:5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here is the convergence of the Ritz values to eigenvalues of $A$."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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5cyf/zSeeeMJqtW7cuJFyQb1ppk6nk2/YgZ+3x+PB71RWVmJDUEoIBoN8C5vQ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\n+F/QIje20oM/FQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"clf\n",
"plot(N+3,lam,'r.')\n",
"hold on\n",
"for n = 4:N\n",
" theta = eig(T(1:n,1:n));\n",
" plot(n,theta,'k.')\n",
"end\n",
"xlabel('n'), ylabel('eigenvalues')\n",
"title('Convergence of Ritz values in Lanczos iteration')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The analog of GMRES in the hermitian case is MINRES, which solves the same least-squares problem on top of the Lanczos iteration. In the case (as here) of a positive definite $A$, there is a convenient theoretical bound on the convergence:\n",
"\n",
"$$ \\frac{\\|r_n\\|}{\\|r_0\\|} \\le 2 \\left( \\frac{\\sqrt{\\kappa}-1}{\\sqrt{\\kappa}+1} \\right)^n,$$\n",
"\n",
"where $\\kappa=\\kappa_2(A)$ equals the ratio of max to min eigenvalues."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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R5qDVap3XMwAAcfCK65BEQh4SoB6ukAcHaLLvh5AmW28orUlNiGZaJBKJXC6/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\nIAoIJAAAEAUEEgAAiML/A7Ncgc5UeuDsAAAAAElFTkSuQmCC\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"resnorm = [];\n",
"for n = 2:N\n",
" yn = T(1:n+1,1:n)\\eye(n+1,1);\n",
" xn = Q(:,1:n)*yn;\n",
" resnorm(n) = norm(b-A*xn);\n",
"end\n",
"clf\n",
"semilogy(resnorm,'.-')\n",
"hold on\n",
"bound = 2*( (sqrt(kappa)-1)/(sqrt(kappa)+1) ).^(0:N);\n",
"plot(0:N,bound,'k--')\n",
"ylim([1e-16 1])\n",
"xlabel('n'), ylabel('||r_n||')\n",
"title('Convergence of MINRES, and an upper bound')"
]
},
{
"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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