[petsc-users] Inverse of a Large Sparse Matrix

[maitri ksh]

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.
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