Contribution to a conference proceedings/Contribution to a book

FZJ-2014-04423

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png The Relation between Galerkin-Type and 1-Norm Quasi-Minimal Residual Iterative Methods

Bücker, H. M. (Corresponding Author)

1998

Abstract: The main ingredients of any Krylov subspace method for the solution of systems of linear equations with nonsingular, in general non-Hermitian coefficient matrix are the generation of a suitable basis and the definition of the actual iterates. Two different strategies for defining the iterates are the Galerkin-type approach and the 1-norm quasi-minimal residual approach. Given any process to form a basis, it is shown that applying the 1-norm quasi-minimal residual approach corresponds to trivial residual smoothing of Galerkin-type iterative methods. An example involving the non-Hermitian Lanczos algorithm without look-ahead as the underlying technique for the generation of a basis is used to illustrate this relationship.

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Contributing Institute(s):

1. Zentralinstitut für Angewandte Mathematik (ZAM)
2. Jülich Supercomputing Center (JSC)

Research Program(s):

1. 899 - ohne Topic (POF2-899) (POF2-899)

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