I have a large sparse matrix (480000x480000) and I need to take its inverse and use it to solve an eigenvalue problem. According to petsc-archive <https://petsc-users.mcs.anl.narkive.com/7sQ6UN4e/sparse-matrix-inversion-using-petsc>, Barry suggested using superLU with MatMatSolve() (& not KSPsolver) for matrix sizes of 5000 to 20000. I was wondering two things: a) is it possible to avoid taking the explicit inverse of the large sparse matrix (as was discussed in the archive) for this particular case (in which I am using the matrix-inverse for an eigenvalue problem) b) is KSPsolver more suitable here?
Also, can someone please explain why SuperLU (SuperLU_SEQUENTIAL, which does not involve any parallel computation) is more efficient in dealing with large sparse matrices as compared to MATLAB's inbuilt LU <https://www.mathworks.com/help/matlab/ref/lu.html> solver.