%0 Conference Paper
%A Bücker, H. Martin
%T The Relation between Galerkin-Type and 1-Norm Quasi-Minimal Residual Iterative Methods
%V 2
%M FZJ-2014-04423
%P 10 p.
%D 1998
%< Proceedings of the 5th Copper Mountain Conference on Iterative Methods
%X 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.
%B 5th Copper Mountain Conference on Iterative Methods
%C 30 Mar 1998 - 3 Apr 1998, Copper Mountain (USA)
Y2 30 Mar 1998 - 3 Apr 1998
M2 Copper Mountain, USA
%F PUB:(DE-HGF)8 ; PUB:(DE-HGF)7
%9 Contribution to a conference proceedingsContribution to a book
%U https://juser.fz-juelich.de/record/155249