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 Post subject: Solver for symmetric, hermitian, real, sparse Linear System
PostPosted: Fri Nov 08, 2019 4:21 pm 
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I have a 2D-FEM-simulation and want to solve the linear equation system Ax = b for it.
Hence, my matrix is
- quadratic
- symmetric
- hermitian
- real
- sparse as on https://en.wikipedia.org/wiki/Sparse_matrix

Which solver is the best for my matrix?
And could you maybe give me a codesnippet of how to code it in C# beginning with:
Code:
alglib.sparsematrix s;

sparsesolvesks(...) works, but is not pretty fast ...


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 Post subject: Re: Solver for symmetric, hermitian, real, sparse Linear Sys
PostPosted: Mon Nov 11, 2019 8:20 am 
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Joined: Fri May 07, 2010 7:06 am
Posts: 855
1. How many variables do you have?
2. How many non-zero elements per entire matrix do you have?


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 Post subject: Re: Solver for symmetric, hermitian, real, sparse Linear Sys
PostPosted: Mon Nov 11, 2019 8:56 am 
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1. around 5000x5000 matrix
2. around 10 non-zero-elements per row


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 Post subject: Re: Solver for symmetric, hermitian, real, sparse Linear Sys
PostPosted: Tue Nov 12, 2019 9:02 am 
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Did you try sparselu() function?

Ideally, you should use Cholesky for positive definite matrices - but presently we do not have sparse Cholesky in ALGLIB, it is planned to be included in version 3.17.0 (we have a lot of stuff in upcoming 3.16.0 which will benefit from sparse Cholesky, so it is of high priority for us).


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 Post subject: Re: Solver for symmetric, hermitian, real, sparse Linear Sys
PostPosted: Thu Nov 14, 2019 7:58 am 
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Yes, Cholesky would be very nice and I am very interested in implementing this to ALGLIB :)


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 Post subject: Re: Solver for symmetric, hermitian, real, sparse Linear Sys
PostPosted: Fri Nov 15, 2019 12:43 pm 
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How do i get a row permutation matrix and a column permutation matrix?


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 Post subject: Re: Solver for symmetric, hermitian, real, sparse Linear Sys
PostPosted: Fri Nov 15, 2019 2:29 pm 
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alglib::sparselu returns them in parameters p and q, as product of individual permutations (see subroutine comments for exact format)


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