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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Lecture 37: Conjugate gradients\n",
"\n",
"When $A$ is hermitian and positive definite, a famous method is available: conjugate gradients. There is a lot to say about CG overall, but to us it is a Krylov subspace method that minimizes a quantity other than the residual over $\\mathcal{K}_n$. This quantity is $\\|\\epsilon_n\\|_A$, where $\\epsilon_n=A^{-1}b-x_n$ is the error and the norm is defined by $\\|u\\|_A^2=u^*Au$. \n",
"\n",
"We won't use the iteration formulas here, just MATLAB's implementation of `pcg`. "
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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",
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x31f0e0f50>)"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"using KrylovMethods\n",
"using PyPlot\n",
"m = 500;\n",
"kappa = 10;\n",
"lam = linspace(1,kappa,m);\n",
"A = sparse(diagm(lam));\n",
"b = randn(m);\n",
"b = b/norm(b);\n",
"\n",
"(xCG,~,~,~,resnorm) = cg(A,b,tol=1e-14,maxIter=100);\n",
"semilogy(resnorm,\".-\");\n",
"ylim(1e-16,1);\n",
"xlabel(\"n\");\n",
"title(\"Convergence of CG\");\n",
"ylabel(L\"\\|r_n\\|_2\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this simple problem, we can calculate the true solution and therefore the error as well."
]
},
{
"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 0x31f4ef0d0>)"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = b./diag(A);\n",
"Anorm(x) = sqrt(dot(x,A*x));\n",
"Aerr = [Anorm(x);zeros(100)];\n",
"for n = 1:100\n",
" (xCG,~,~,~,resnorm) = cg(A,b,tol=1e-14,maxIter=n,out=-1);\n",
" Aerr[n+1] = Anorm(x-xCG);\n",
"end\n",
"\n",
"(xCG,~,~,~,resnorm) = cg(A,b,tol=1e-14,maxIter=100);\n",
"semilogy(resnorm,\".-\");\n",
"semilogy(Aerr,\".-\");\n",
"ylim(1e-16,1);\n",
"xlabel(\"n\");\n",
"title(\"Convergence of CG\");\n",
"text(50,1e-10,L\"\\|r_n\\|_2\");\n",
"text(30,1e-13,L\"\\|\\epsilon_n\\|_A\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Effect of condition number\n",
"\n",
"We already know that a large $\\kappa(A)$ creates error in the solution of $Ax=b$. But it carries another penalty in Krylov methods: slower convergence. We have essentially the same result for CG as for MINRES, but using the $A$-norm of the errors:\n",
"\n",
"$$ \\frac{\\|\\epsilon_n\\|}{\\|\\epsilon_0\\|} \\le 2 \\left( \\frac{\\sqrt{\\kappa}-1}{\\sqrt{\\kappa}+1} \\right)^n,$$\n",
"\n",
"where $\\kappa=\\kappa_2(A)$ equals the ratio of max to min eigenvalues."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x31f9f0850>)"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"PyObject <matplotlib.text.Text object at 0x31fa0eb90>"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"for kappa = [10 100 1000 1e4]\n",
" bound = 2*( (sqrt(kappa)-1)/(sqrt(kappa)+1) ).^(0:100);\n",
" semilogy(0:100,bound*Aerr[1]);\n",
"end\n",
"ylim(1e-16,1)\n",
"text(60,1e-15,L\"\\kappa=10\")\n",
"text(95,1e-8,L\"\\kappa=10^2\")\n",
"text(95,1e-3,L\"\\kappa=10^3\")\n",
"text(95,1e-1,L\"\\kappa=10^4\")\n",
"title(\"Effect of conditioning on convergence\")\n",
"xlabel(\"n\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The effect is the same for MINRES and CG, but measured in different terms. In particular, CG does *not* guarantee a nonincreasing residual norm."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x31feee550>)"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"kappa = 1e4;\n",
"lam = linspace(1,kappa,m);\n",
"A = sparse(diagm(lam));\n",
"b = randn(m);\n",
"b = b/norm(b);\n",
"(xCG,~,~,~,resnorm) = cg(A,b,tol=1e-14,maxIter=100,out=-1);\n",
"semilogy(resnorm,\".-\")\n",
"text(60,0.3,\"CG\")\n",
"(xMR,~,~,~,resnorm) = gmres(A,b,m,tol=1e-14,maxIter=100);\n",
"semilogy(resnorm,\".-\");\n",
"text(40,.0075,\"MINRES\");\n",
"xlim(0,100);\n",
"ylim(1e-4,1);\n",
"xlabel(\"n\");\n",
"title(L\"Convergence for $\\kappa=10^4$\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"CG and MINRES are often not much different, practically speaking. MINRES also works for indefinite problems, while CG has considerably more (or at least better-known) theory behind it."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 0.5.0",
"language": "julia",
"name": "julia-0.5"
},
"language_info": {
"file_extension": ".jl",
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}
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