Divide and Conquer Low-rank Preconditioning Techniques

This paper presents a preconditioning method based on a recursive multilevel lowrank approximation approach. The basic idea is to recursively divide the problem into two and apply a low-rank approximation to a matrix obtained from the Sherman-Morrison formula. The low-rank approximation may be computed by the partial Singular Value Decomposition (SVD) or it can be approximated by the Lanczos bidiagonalization method. This preconditioning method is designed for handling different levels of parallelism on multi-processor systems of multi(many)-core processors. Numerical experiments indicate that, when combined with Krylov subspace accelerators, this method can be efficient and robust for solving symmetric indefinite sparse linear systems.