TY  - JOUR
T1  - On the Convergence of QOR and QMR Krylov Methods for Solving Nonsymmetric Linear Systems
A1  - Duintjer Tebbens, Jurjen
A1  - Meurant, Gérard
JA  - BIT Numerical Mathematics
Y1  - 2015
KW  - Q-OR method · Q-MR method · BiCG · QMR · CMRH · eigenvalue influence · prescribed convergence
N2  - This paper addresses the convergence behavior of Krylov methods for nonsymmetric linear systems which can be classified as Q-OR (quasiorthogonal) or Q-MR (quasi-minimum residual) methods. It explores, more precisely, whether the influence of eigenvalues is the same when using nonorthonormal bases as it is for the FOM and GMRES methods. It presents parametrizations of the classes of matrices with a given spectrum and righthand sides generating prescribed Q-OR/Q-MR (quasi) residual norms and discusses non-admissible residual norm sequences. It also gives closed-form expressions of the Q-OR/Q-MR (quasi) residual norms as functions of the eigenvalues and eigenvectors of the matrix of the linear system.
M1  - Preprint project = NCMM
M1  - Preprint year = 2015
M1  - Preprint number = 13
M1  - Preprint ID = NCMM/2015/13
ER  -