Skip to content

Instantly share code, notes, and snippets.

@tobydriscoll
Last active February 26, 2021 17:18
Show Gist options
  • Star 1 You must be signed in to star a gist
  • Fork 0 You must be signed in to fork a gist
  • Save tobydriscoll/204bbc93b984c9ddf17bbe51e162399d to your computer and use it in GitHub Desktop.
Save tobydriscoll/204bbc93b984c9ddf17bbe51e162399d to your computer and use it in GitHub Desktop.
TB_Lecture33
Display the source blob
Display the rendered blob
Raw
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Lecture 33: Arnoldi iteration\n",
"\n",
"Suppose $A\\in\\mathbb{C}^{m\\times m}$ and $b\\in\\mathbb{C}^m$ are given. The $n$th **Krylov subspace** $\\mathcal{K}_n$ is the range of a certain $m\\times n$ matrix:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"A = randn(500,500);\n",
"b = ones(500,1);\n",
"K = b;\n",
"n = 10;\n",
"for j = 1:n-1\n",
" K = [K A*K[:,j]];\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"One way to think of $K$ is as keeping a history of all the vectors found in the power iteration. For that reason, we suspect that it may be rich in content with the leading eigenvectors of $A$, much as with simultaneous iteration. However, it's a poorly conditioned basis as $n$ grows, since the columns all become parallel to the leading eigenvector."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"1.4672383709343213e12"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cond(K)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We'd like a (thin) QR factorization of $K$, of course, but once $K$ has been put into floating point, the information about successive dimensions could be drawn out only through subtractive cancellation. Instead, there is a clever way to arrange the Gram-Schmidt process for this particular matrix.\n",
"\n",
"Say $q_1,\\ldots,q_j$ is an ONB for $\\mathcal{K}_j$. By construction, $Aq_j\\in \\mathcal{K}_{j+1}$. Thus if $q_{j+1}$ extends the ONB to $\\mathcal{K}_{j+1}$, it must be that\n",
"\n",
"$$Aq_j = h_{1j} q_1 + \\cdots + h_{nj} q_n + h_{j+1,j} q_{j+1}.$$\n",
"\n",
"Furthermore, $h_{ij}=q_i^*Aq_j$. Written out for all $j=1,\\ldots,n$, this implies \n",
"\n",
"$$AQ_n = Q_{n+1} \\tilde{H}_n,$$\n",
"\n",
"where $Q_j$ collects $q_1,\\ldots,q_j$ and $\\tilde{H}_n$ is an $(n+1)\\times n$ upper Hessenberg matrix. Adapting the modified Gram-Schmidt algorithm, where the \"new column\" of a matrix comes from $A$ times the most recent column, we get the **Arnoldi iteration**."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"m = size(A,1); n = 50;\n",
"Q = zeros(m,n+1);\n",
"H = zeros(n+1,n);\n",
"Q[:,1] = b/norm(b);\n",
"for j = 1:n\n",
" v = A*Q[:,j];\n",
" for i = 1:j\n",
" H[i,j] = dot(Q[:,i],v);\n",
" v = v - H[i,j]*Q[:,i];\n",
" end\n",
" H[j+1,j] = norm(v);\n",
" Q[:,j+1] = v/H[j+1,j];\n",
"end"
]
},
{
"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 0x32e6b4c50>)"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"using PyPlot\n",
"spy(H);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It's not hard to show that we can project $A$ into $\\mathcal{K}_n$ (in the $Q_n$-basis) by \n",
"\n",
"$$Q_n^*AQ_n = Q_n^*Q_{n+1}\\tilde{H}_n = H_n,$$\n",
"\n",
"where $H_n$ is $\\tilde{H}_n$ with the last row deleted. Eigenvalues of $H_n$ are eigenvalues of the action of $A$ as projected to $\\mathcal{K}_n$. As $n\\to\\infty$, this begins to reveal some of the eigenvalues of $A$ itself. "
]
},
{
"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 0x32e7d0310>)"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"lam = eigvals(A);\n",
"plot(real(lam),imag(lam),\".\")\n",
"axis(\"square\")\n",
"axis(\"equal\")\n",
"for j = 5:n\n",
" lam = eigvals(H[1:j,1:j]);\n",
" plot(real(lam),imag(lam),\"rx\")\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We'll look more closely at the convergence in the next lecture. For now, the big idea is to replace a problem on a very high-dimensional space, $\\mathbb{C}^m$, with an analog on a low-dimensional space, $\\mathcal{K}_n$, using a ON basis as provided by the Arnoldi iteration."
]
}
],
"metadata": {
"anaconda-cloud": {},
"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
}
Display the source blob
Display the rendered blob
Raw
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