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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 Duintjer Tebbens, Jurjen
Meurant, Gérard
Added by: [JP]
Total mark: 0
Attachments
  • 20151229080856.pdf
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