There are lots of nice methods to solve systems of linear equations using Krylov subspaces, for example BiCGSTAB or GMRES. I noticed, this was briefly mentioned in @gnzlbg’s wishlist for HPC, so I thought it would be good to reach out to the community before jumping straight into implementation. In my field, people seem to be using PETSc, an MPI-based C library of all sorts of HPC algorithms, for this purpose.
Has anyone been working on this? I have not found anything open-sourced yet anyway. I will probably work on one of these algorithms in a generic fashion, so that they can be used with different matrix implementations. I am thinking of sparse matrices, matrices distributed across different nodes, etc.