Skip to content

Instantly share code, notes, and snippets.

Embed
What would you like to do?
{
"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": [
{
"data": {
"text/plain": [
"5×5 Array{Float64,2}:\n",
" 5.64535 2.71461 0.0 0.0 0.0 \n",
" 2.71461 5.35048 2.26433 0.0 0.0 \n",
" 0.0 2.26433 5.35529 2.3172 0.0 \n",
" 0.0 0.0 2.3172 5.65767 2.25477\n",
" 0.0 0.0 0.0 2.25477 5.47117"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"include(\"Krylov.jl\")\n",
"m = 400;\n",
"kappa = 10;\n",
"N = 60;\n",
"lam = linspace(1,kappa,m);\n",
"A = diagm(lam);\n",
"b = randn(m);\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": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x324816f50>)"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"PyObject <matplotlib.text.Text object at 0x3249e0850>"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using PyPlot\n",
"nn = ones(m);\n",
"plot([N+3],lam',\"r.\")\n",
"for n = 4:N\n",
" theta = eigvals(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": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x327302e10>)"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"resnorm = zeros(N);\n",
"for n = 2:N\n",
" yn = T[1:n+1,1:n]\\[1;zeros(n)];\n",
" xn = Q[:,1:n]*yn;\n",
" resnorm[n] = norm(b-A*xn);\n",
"end\n",
"semilogy(resnorm,\".-\");\n",
"\n",
"bound = 2*( (sqrt(kappa)-1)/(sqrt(kappa)+1) ).^(0:N);\n",
"semilogy(0:N,bound,\"k--\");\n",
"\n",
"ylim(1e-16,1);\n",
"xlabel(L\"n\"), ylabel(L\"\\|r_n\\|\");\n",
"title(\"Convergence of MINRES, and an upper bound\");"
]
}
],
"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
}
Sorry, something went wrong. Reload?
Sorry, we cannot display this file.
Sorry, this file is invalid so it cannot be displayed.
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment