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

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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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Accepted Answer

Christine Tobler
Christine Tobler on 5 Dec 2018

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Youngsuk Jung
Youngsuk Jung on 6 Dec 2018
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?
Christine Tobler
Christine Tobler on 6 Dec 2018
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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