[sdhsami]

Dear all
I wish to solve a linear system with a 4000*4000 symmetric sparse matrix.
I was wondering what iterative method could be the best choice so that solving takes the least time?
Thanks

[kaya]

I don't have enough experience on these but the one who has, perhaps going to need more information than your matrix size Perhaps knowing actual physics in the system, magnitude of required residual or parallel / sequential computing etc. will change the answer of your question.

If your system is 3 diagonal you can go with this algorithm called 'TDMA (3-diag-matrix-algorthm)'. Thats a quite efficient way of direct solving 3diag systems, which is no more than looping 1-->4000 & 4000-->1 with about 3-4 floating point operations in each if Im not mistaken.

[FMDenaro]

Originally Posted by sdhsami

Dear all
I wish to solve a linear system with a 4000*4000 symmetric sparse matrix.
I was wondering what iterative method could be the best choice so that solving takes the least time?
Thanks

that means you have only 4000 unknowns, even the simple Jacobi is suitable for such problem... you have diagonal dominance?

usually, I solve for some millions of unknown with SOR, you do not need to store the entire matrix

[metu_aee]

such system corresponds to very small problem in cfd actually. for those small problems direct methods converges very rapidly. iterative methods are better in larger problems but whatever if you go through the iterative methods than projection based methods, krylov subspace methods are suitable. such as gmres. you can look for detail yousef saad's book iterative methods for sparse linear systems.