Volume 60, pp. 40-58, 2024.

The stability of split-preconditioned FGMRES in four precisions

Erin Carson and Ieva Daužickaitė


We consider the split-preconditioned FGMRES method in a mixed-precision framework, in which four potentially different precisions can be used for computations with the coefficient matrix, application of the left preconditioner, application of the right preconditioner, and the working precision. Our analysis is applicable to general preconditioners. We obtain bounds for the backward and forward errors in the split-preconditioned FGMRES method. Our analysis further provides insight into how the various precisions should be chosen; under certain assumptions, a suitable selection guarantees a backward error of the order of the working precision.

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Key words

mixed precision, FGMRES, iterative methods, roundoff error, split-preconditioned

AMS subject classifications

65F08, 65F10, 65F50, 65G50, 65Y99

Links to the cited ETNA articles

[4]Vol. 33 (2008-2009), pp. 31-44 M. Arioli and I. S. Duff: Using FGMRES to obtain backward stability in mixed precision

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