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Persistent URL http://purl.org/net/epubs/work/50389
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Record Id 50389
Title Using FGMRES to obtain backward stability in mixed precision
Abstract We consider the triangular factorization of matrices in single-precision arithmetic and show how these factors can be used to obtain a backward stable solution. Our aim is to obtain double-precision accuracy even when the system is ill-conditioned. We examine the use of iterative refinement and show by example that it may not converge. We then show both theoretically and practically that the use of FGMRES will give us the result that we desire with fairly mild conditions on the matrix and the direct factorization. We perform extensive experiments on dense matrices using MATLAB and indicate how our work extends to sparse matrix factorization and solution.
Organisation CSE , CSE-NAG , STFC
Keywords GMRES , Roundoff
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Language English (EN)
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Journal Article Electronic Transactions on Numerical Analysis 33 (2009): 31-44. Is in proceedings of: Conference on Matrix Analysis and Applications held Honor of Gerard Meurant, Luminy, France, 15 october 2007. ETNA-33-2009-ArioliDuff.pdf 2009