On the Convergence of QOR and QMR Krylov Methods for Solving Nonsymmetric Linear Systems
| Type of publication: | Article |
| Citation: | |
| Publication status: | Submitted |
| Journal: | BIT Numerical Mathematics |
| Year: | 2015 |
| Abstract: | 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. |
| Preprint project: | NCMM |
| Preprint year: | 2015 |
| Preprint number: | 13 |
| Preprint ID: | NCMM/2015/13 |
| Keywords: | Q-OR method · Q-MR method · BiCG · QMR · CMRH · eigenvalue influence · prescribed convergence |
| Authors | |
| Added by: | [JP] |
| Total mark: | 0 |
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