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A new variant of restarted GMRES
Author(s) -
Simoncini V.
Publication year - 1999
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/(sici)1099-1506(199901/02)6:1<61::aid-nla146>3.0.co;2-w
Subject(s) - generalized minimal residual method , convergence (economics) , monotonic function , mathematics , eigenvalues and eigenvectors , simple (philosophy) , polynomial , smoothness , mathematical optimization , iterative method , linear system , computer science , algorithm , mathematical analysis , philosophy , physics , epistemology , quantum mechanics , economics , economic growth
GMRES is an attractive iterative method for solving large non‐symmetric algebraic linear systems. Computational and storage constraints usually force the method to be restarted after a fixed (small) number of iterations with subsequent loss of monotonic convergence properties. Trouble may be caused by the presence of eigenvalues close to the origin which are not well detected by early restarts. Unlike recent techniques that propose to include this information in later restarts, we use a new formulation of GMRES to derive a simple variant of the algorithm. The new approach attempts to mitigate stagnation by exploiting the smoothness of a certain polynomial near zero, resorting to the original method once convergence becomes truly monotonic. Copyright © 1999 John Wiley & Sons, Ltd.