I am trying to solve computationally a sparse linear system of the form $Ax=B.$
A is a square matrix, for example of size $1600\times 1600$ (the exact size depends on the parameters of my program). B is a dense matrix, of size $1600\times 2$ or $1600\times3$.
I am trying, obviously, to solve for $x$.
The best general purpose sparse linear solver I could find is Paradiso, based on Intel MKL, which solves this system in about $100ms$.
Unfortunately, this is a bit too much time for the performance I would like for my system, so I'm looking for ways to improve.
The matrix A has quite a lot of structure. It is basically a set of $7$ lines of nonzero values running parallel to the main diagonal, as you can see in the heatmaps below:
Is there any way to use this structure to solve the system easier?