Ax = b for a lot of different b‘s
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Hello,
I have a system of equation Ax = b, where A is very large (n = 3e5 - 8e5) and sparse coefficient matrix, b is source term and x is the solution. Of course it's not a problem to solve such a problem in MATLAB, however I have to solve Ax = b for a lot of different b‘s without any change in the coefficient matrix A. The inversion of the matrix A take so long, that it is faster to solve the problem for each new b vector separately using an iterative solver. Unfortunately it is still way too slow, so I'm looking for a way how to speed it up.
Does anybody know, how to improve the performance?
Thank you for help!
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Matt J
2013 年 4 月 18 日
編集済み: Matt J
2013 年 4 月 18 日
Neither direct inversion of A, nor iterative methods are required. Just create a matrix B whose columns are the different b. Then do
X=A\B
Each column X(:,i) will be the solution for the corresponding b.
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Matt J
2013 年 4 月 19 日
編集済み: Matt J
2013 年 4 月 19 日
well it really helps! I have lost some control, e.g. precision, parralelization or preconditioning
Not sure why you feel you've lost precision or why you think pre-conditioning matters when you're using a non-iterative method. It's true you have no control over the parallelization, but parallelization is done for you internally by MLDIVIDE.
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