Solving the arising equation with preconditioned iteration method.

Question

Ziwen Gu 2023-12-19

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https://ww2.mathworks.cn/matlabcentral/answers/2061982-solving-the-arising-equation-with-preconditioned-iteration-method

评论： Ziwen Gu 2023-12-20

采纳的回答： John D'Errico

I want to use preconditioned iteration method, like pcg or gmres, to solve

.

In each iteration, it has to solve some additional linear equation with

, where M is a selected preconditioner for A.

My question is:

What method will Matlab use to solve the arising eqution ?
Based on the structure of M, I have a quick method to solve , how can I use my method instead of the defaulted one?
Can I get souce code for pcg and gmres?(I tried and failed, because Matlab is not open sourced?) In this way I can write that part of code by myself.

Thanks a lot for your help!

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Answer 1

John D'Errico 2023-12-20

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https://ww2.mathworks.cn/matlabcentral/answers/2061982-solving-the-arising-equation-with-preconditioned-iteration-method#answer_1374527

编辑：John D'Errico 2023-12-20

在 MATLAB Online 中打开

I'm not sure what you are talking about. BOTH PCG and GMRES are written in MATLAB itself. So the source code is provided to you. All you had to do was look.

Should you modify the code? NO! At least, if you do, then make a copy of it, with a new name. Do NOT modify the code and leave the name unchanged.

Can you provide your own solver? READ THE HELP! Here is the pertinent part:

X = PCG(A,B,TOL,MAXIT,M) and X = PCG(A,B,TOL,MAXIT,M1,M2) use the 
%   symmetric positive definite preconditioner M or M = M1*M2 and
%   effectively solve the symmetric system inv(H)*A*inv(H')*Y = inv(H)*B
%   for Y, where Y = H'*X and M = H*H'. The algorithm does not form H
%   explicitly. If M is [] then a preconditioner is not applied. M may be a
%   function handle MFUN returning M\X.

So you can provide a function handle that does the work.