The stability of split-preconditioned FGMRES in four precisions

03/21/2023

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by   Erin Carson, et al.

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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, and application of the right preconditioner, and the working precision. Our analysis is applicable to general preconditioners. We obtain bounds on the backward and forward errors in split-preconditioned FGMRES. Our analysis further provides insight into how the various precisions should be chosen; a suitable selection guarantees a backward error on the order of the working precision.