I am solving the linear system $Ax = b$, where $A \in C^{n\times n}$, $b \in C^{n\times 1}$. A is a sparse, non-diagonally dominant & non-symmetric matrix.
I have a good estimate, although not an exact solution, of the k-rank SVD of the matrix $A^{-1}$. Where, $k << n$ i.e I have a good estimate of the $k$ smallest singular values (and their associated vectors) of $A$ i.e a good estimate of the $k$ largest singular values (and their associated vectors) of the matrix $A^{-1}$.
Is there a method where I can use this information I have about the SVD to help me solve the linear system? Either through using it as a pre-conditioner for an iterative solver, or otherwise.
Thanks!