Conjugate Gradient Method 1.0

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-contionedb=randn(1000,1);tic,x=conjgrad(A,b);toctic,x1=Ab;tocnorm(x-x1)norm(x-A*b)Conjugate gradient is about two to three times faster than Ab, which uses the Gaissian elimination.

Requirements:	No special requirements
Platforms:	Matlab
Keyword:	Approach,  Elimination,  Examplen Usv Dsvdrandnns Ddiagsa Dudiags Bmaxsu,  Faster,  Gaissian,  Gaussian,  Large,  Linear,  Scale,  Suitable,  Systemsit,  Times,  Wellconditioned
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