GMERR - an Error Minimizing Variant of GMRES

Abstract

The paper analyzes a recently proposed iterative error minimizing method for the solution of linear systems. Sufficient and necessary conditions for convergence are studied, which show that the method essentially requires normal matrices. An efficient implementation similar to GMRES has been worked out in detail. Numerical tests on general non--normal matrices, of course, indicate that this approach is not competitive with GMRES. Summarizing, if error minimizing is important, one should rather choose CGNE. A computational niche for GMERR might be problems, where normal but non--symmetric matrices occur, like dissipative quantum mechanics. AMS Subject Classification: 65F10, 65F25, 65F50 Keywords: linear systems, Krylov subspace methods, error minimizing methods, preconditioning Contents 1 Introduction 1 2 Derivation of the method 1 3 Convergence analysis of GMERR 3 4 Algorithmic realization 8 5 Convergence control of GMERR 10 6 Numerical tests 11 References 13 Appendix 1: Iterative..