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What is the best method to solve large linear system equation (Ax=b) (A:million~ by million~)

Asked by Youngsuk Jung on 5 Dec 2018
Latest activity Commented on by Christine Tobler on 6 Dec 2018
The maxtix A is sparse from finite element analysis.
I have used backslash to solve the equation but I want to reduce the calculation time.
I also tried to use GPU acceleration but there is a memory limitation with Titan xp with 12Gb memory.

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Answer by Christine Tobler on 5 Dec 2018
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As I know, Matlab choose appropriate method to solve linear equation when I use backslash(\).
Is there any chance to improve the performance by using Iterative solve myself?
Why? MATLAB has also a bunch of iterative solvers to chose from: cgs, bicg, gmres, etc...
MATLAB chooses an appropriate direct solver in backslash. Using iterative solvers requires more trial and error, and more knowledge of the original system (as preconditioners are often necessary). For a large, well-conditioned matrix, there can be a significant speed-up compared to backslash, if a suitable iterative solver is used.

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