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• W2153179908 abstract "Flexible Krylov methods refers to a class of methods which accept preconditioning that can change from one step to the next. Given a Krylov subspace method, such as CG, GMRES, QMR, etc. for the solution of a linear system Ax=b, instead of having a fixed preconditioner M and the (right) preconditioned equation AM-1y = b (Mx =y), one may have a different matrix, say Mk, at each step. In this paper, the case where the preconditioner itself is a Krylov subspace method is studied. There are several papers in the literature where such a situation is presented and numerical examples given. A general theory is provided encompassing many of these cases, including truncated methods. The overall space where the solution is approximated is no longer a Krylov subspace but a subspace of a larger Krylov space. We show how this subspace keeps growing as the outer iteration progresses, thus providing a convergence theory for these inner-outer methods. Numerical tests illustrate some important implementation aspects that make the discussed inner-outer methods very appealing in practical circumstances." @default.
• W2153179908 created "2016-06-24" @default.
• W2153179908 creator A5047875137 @default.
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• W2153179908 date "2002-01-01" @default.
• W2153179908 modified "2023-10-18" @default.
• W2153179908 title "Flexible Inner-Outer Krylov Subspace Methods" @default.
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• W2153179908 doi "https://doi.org/10.1137/s0036142902401074" @default.
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