TY  - CONF
AU  - Bücker, H. Martin
TI  - The Relation between Galerkin-Type and 1-Norm Quasi-Minimal Residual Iterative Methods
VL  - 2
M1  - FZJ-2014-04423
SP  - 10 p.
PY  - 1998
AB  - 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.
T2  - 5th Copper Mountain Conference on Iterative Methods
CY  - 30 Mar 1998 - 3 Apr 1998, Copper Mountain (USA)
Y2  - 30 Mar 1998 - 3 Apr 1998
M2  - Copper Mountain, USA
LB  - PUB:(DE-HGF)8 ; PUB:(DE-HGF)7
UR  - https://juser.fz-juelich.de/record/155249
ER  -