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Numerical experiments on a flexible variant of GMRES‐DR
Author(s) -
Giraud Luc,
Gratton Serge,
Pinel Xavier,
Vasseur Xavier
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700097
Subject(s) - generalized minimal residual method , krylov subspace , eigenvalues and eigenvectors , convergence (economics) , mathematics , linear system , computer science , iterative method , algorithm , mathematical analysis , physics , quantum mechanics , economics , economic growth
Abstract The Flexible GMRES (FGMRES [1]) and the GMRES with deflated restarting (GMRES‐DR [2]) methods are two algorithms derived from GMRES [3], that are considered as powerful when solving large non hermitian systems of linear equations. GMRES‐DR is a variant of GMRES with an improved restarting technique that maintains in the Krylov subspace harmonic Ritz vector from the previous restart. In situations where the convergence of restarted GMRES is slow and where the matrix has few eigenvalues close to the origin, this technique has proved very efficient. The new method that we propose is the Flexible GMRES with deflated restarting (FGMRES‐DR [6]), which combines the two above mentioned algorithms in order to yield better performance. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)