Conjugate Gradient Method
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The conjugate gradient method aims to solve a system of linear equations, Ax=b, where A is symmetric, without calculation of the inverse of A. It only requires a very small amount of membory, hence is particularly suitable for large scale systems.
It is faster than other approach such as Gaussian elimination if A is well-conditioned. For example,
n=1000;
[U,S,V]=svd(randn(n));
s=diag(S);
A=U*diag(s+max(s))*U'; % to make A symmetric, well-contioned
b=randn(1000,1);
tic,x=conjgrad(A,b);toc
tic,x1=Ab;toc
norm(x-x1)
norm(x-A*b)
Conjugate gradient is about two to three times faster than Ab, which uses the Gaissian elimination.
Free download from Shareware Connection - The conjugate gradient method aims to solve a system of linear equations, Ax=b, where A is symmetric, without calculation of the inverse of A
Version: 1.0 | Size: 10 KB | Platform: Matlab, Scripts
Released Date: 16-02-2013 | Rating: 0 | Title: Conjugate Gradient Method
Author Url: http://www.mathworks.com
Program Info Url: http://www.mathworks.com
Download Url: http://www.mathworks.com/matlabcentral/fx_files/22494/2/conjgrad.zip
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