TY  - RPRT
AU  - Bücker, H. Martin
TI  - A transpose-free 1-norm quasi-minimal residual algorithm for non-Hermitian linear systems
IS  - FZJ-ZAM-IB-9706
M1  - FZJ-2014-04421
M1  - FZJ-ZAM-IB-9706
SP  - 14 p.
PY  - 1997
AB  - The transpose-free quasi-minimal residual method (TFQMR) for solving general non-Hermitian linear systems makes use of the conjugate gradient squared algorithm (CGS) to generate the underlying Krylov subspaces. By incorporating the quasi-minimal residual approach, TFQMR produces a smooth and nearly monotone convergence behavior in the residual norm thus remedying the rather irregularly oscillating convergence behavior of CGS. While in TFQMR the quasi-minimal residual approach involves minimization in the Euclidean norm, this note proposes a different, yet similar approach by minimizing with respect to the 1-norm. It is shown that this new approach can be used to obtain a CGS-like iterative process based on short recurrences with a smooth and regular convergence behavior. The resulting transpose-free 1-norm quasi-minimal residual method (TFQMR_1) does not involve matrix-by-vector products with the transpose of the coefficient matrix and can be implemented very easily either from CGS or TFQMR. Numerical experiments are reported demonstrating that TFQMR_1 is particularly attractive for very large systems because the norm of the residual vector is explicitly available during the course of the computation.
LB  - PUB:(DE-HGF)15
UR  - https://juser.fz-juelich.de/record/155247
ER  -