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 on the backward and forward errors in split-preconditioned FGMRES. Our analysis further provides insight into how the various precisions should be chosen; under certain assumptions, a suitable selection guarantees a backward error on the order of the working precision.

翻译：本文研究混合精度框架下的分裂预处理FGMRES方法，该框架允许对系数矩阵计算、左预处理器应用、右预处理器应用及工作精度采用四种可能不同的精度。我们的分析适用于一般预处理器，推导出分裂预处理FGMRES的向后误差与向前误差界限。进一步地，分析揭示了各精度应如何选取：在特定假设下，恰当的精度选择可保证向后误差达到工作精度量级。