Mikko Byckling: January 13, 2011

Preconditioning for standard and two-sided Krylov subspace methods

Mikko Byckling,  Aalto University, Finland and CERFACS, France

Thursday, January 13, 15:00 p.m. in the CERFACS conference room

Abstract:

This talk is concerned with the solution of large nonsymmetric sparse linear systems. The main focus is on iterative solution methods and preconditioning. Assuming the linear system has a special structure, a minimal residual method called TSMRES, based on a generalization of a Krylov subspace, is presented and its convergence properties studied. In numerical experiments it is shown that there are cases where the convergence speed of TSMRES is faster than that of GMRES and vice versa. The numerical implementation of TSMRES is studied and a new numerically stable formulation is presented. In addition it is shown that preconditioning general linear systems for TSMRES by splittings is feasible in some cases. Finally, a new approach to compute a factorized approximate inverse of a matrix suitable for preconditioning is presented.