What is the next step after LU decomposition for solving Ax=b?

[Milentije]

I have
Ax=b problem
where A 1484x1484 matrix,b 1484x1.
A is sparse(95% zeros) but if I go for LU decomposition what should be the next step?
Or is there any other method,I forgot algebra,learned it when I was undergrad long time ago.

 

[hilbert2]

Simple Gauss elimination is mainly a pedagogical tool used in teaching linear systems, and it's far from being the most effective method (especially when talking about specialized problems like sparse systems). If you're writing a code that solves your linear system, you can find free open source libraries/software packages for that. Just Google "sparse linear system open source".

 

[Mandelbroth]

I have
Ax=b problem
where A 1484x1484 matrix,b 1484x1.
A is sparse(95% zeros) but if I go for LU decomposition what should be the next step?
Or is there any other method,I forgot algebra,learned it when I was undergrad long time ago.

1484?

May I ask what this is for, out of curiosity?

 

[SteamKing]

The best method will depend on several factors. Is A banded and symmetric? If is narrow banded and symmetric, Gauss, Choleski decomp, or other methods may be used. If A is large, sparse, and the zero entries are somewhat randomly distributed, with no symmetry or banded layout of the non-zero terms, then an iterative method might be more suitable.

 

[Milentije]

Yes,I am creating input file where velocities need to be calculated for every node.Total number of velocities in model is 1484,quite big.
Regarding software,I have problem to install SUPER Lu from LBNL,are there any links for simple code that to not require libraries(like BLAS( IN THIS CASE?

 

[SteamKing]

I would make my first stop at the netlib: http://www.netlib.org/

Depending on what method you use, you can always google (or dogpile) and find scads of code.