On Solving Large, Ill Conditioned Linear Systems

Craig C. Douglas M.S. M.Phil. Ph.D.

May 23, 2017, 3:30 p.m. S2 059

This talk presents results to combine theoretically sound methods (spectral
projection, deflation methods, and multigrid methods) together to attack large,
ill conditioned linear systems. Our results show that the proposed algorithm
applied to a Krylov subspace method takes much fewer iterations for solving
ill conditioned problems downloaded from a popular online sparse matrix
collection. To our best knowledge, the constructions of most, if not all,
deflation subspace matrices in the literature are problem dependent. Further,
some of them are ad-hoc. The method proposed here is problem Independent.