Preconditioning for standard and two-sided Krylov subspace methods
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Aalto-yliopiston teknillinen korkeakoulu |
Doctoral thesis (monograph)
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Authors
Date
2010
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Degree programme
Language
en
Pages
Verkkokirja (36384 KB, 176 s.)
Series
Research report.
Helsinki University of Technology, Institute of Mathematics,
A,
597
Abstract
This thesis 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. The direct solution of sparse linear systems of the Hessenberg type is also studied. Finally, a new approach to compute a factorized approximate inverse of a matrix suitable for preconditioning is presented.Description
Keywords
minimal residual methods, Krylov subspaces, nonsymmetric systems, preconditioning, approximate inverses