Iterative Construction of Non-Symmetric Factored Sparse Approximate Inverse Preconditioners

Factored sparse approximate inverses (FSAI) play a key-role in the efficient algebraic preconditioning of sparse linear systems of equations. For SPD problems remarkable results are obtained by building the FSAI non-zero pattern iteratively during its computation [1]. Unfortunately, an equivalent algorithm still is missing in the non-symmetric case. In the present contribution we explore the possibility of iteratively computing FSAI for non-symmetric matrices by using an incomplete Krylov subspace bi-orthogonalization procedure. Another adaptive technique relies on the idea of directly minimizing the two norm of the off-diagonal row(/column) of the preconditioned matrix. Finally, as reference algorithm, a factorized sparse approximate inverse on static pattern is considered. The main idea behind these approaches is to build two real sparse triangular factors (W is lower triangular and Z is upper triangular) such that: