On the Convergence of Q-OR and Q-MR Krylov Methods for Solving Nonsymmetric Linear Systems

0454997 - ÚI 2017 RIV SE eng J - Journal Article
Duintjer Tebbens, Jurjen - Meurant, G.
On the Convergence of Q-OR and Q-MR Krylov Methods for Solving Nonsymmetric Linear Systems.
Bit. Roč. 56, č. 1 (2016), s. 77-97. ISSN 0006-3835. E-ISSN 1572-9125
R&D Projects: GA ČR GA13-06684S
Institutional support: RVO:67985807
Keywords : Krylov method * Q-OR method * Q-MR method * BiCG * QMR * CMRH * eigenvalue influence * prescribed convergence
Subject RIV: BA - General Mathematics
Impact factor: 1.670, year: 2016

This paper addresses the convergence behavior of Krylov methods for nonsymmetric linear systems which can be classified as quasi-orthogonal (Q-OR) or quasi-minimum residual (Q-MR) methods. It explores, more precisely, whether the influence of eigenvalues is the same when using non-orthonormal bases as it is for the FOM and GMRES methods. It presents parametrizations of the classes of matrices with a given spectrum and right-hand 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.
Permanent Link: http://hdl.handle.net/11104/0255656