Using FGMRES to obtain backward stability in mixed precision

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Persistent URL	http://purl.org/net/epubs/work/50389
Record Status	Checked
Record Id	50389
Title	Using FGMRES to obtain backward stability in mixed precision
Contributors	M Arioli (STFC Rutherford Appleton Lab.), IS Duff (STFC Rutherford Appleton Lab.)
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)

Type	Details	URI(s)	Local file(s)	Year
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