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- W4384696501 abstract "We are interested in obtaining solutions to parameterized linear systems of the form for many values of the parameter . Here is large, sparse, and nonsingular with a nonlinear, analytic dependence on . Our approach approximates the solution to a linearized system in a flexible GMRES setting [Y. Saad, SIAM J. Sci. Comput., 14 (1993), pp. 461–469], where the linearization is based on a companion matrix similar to the operator in the infinite Arnoldi method [E. Jarlebring, W. Michiels, and K. Meerbergen, Numer. Math., 122 (2012), pp. 169–195]. This novel approach applies the action of a preconditioner inexactly, providing performance improvement over the method infinite GMRES [Jarlebring and Correnty, SIAM J. Matrix Anal. Appl., 43 (2022), pp. 1382–1405] without a loss of accuracy in general. The method returns a function which is cheap to evaluate for different . We show that the error of our method is estimated based on the magnitude of the parameter , the inexactness of the preconditioning, and the spectrum of the companion matrix. Numerical examples from a finite element discretization of a Helmholtz equation with a parameterized material coefficient illustrate the competitiveness of our approach. The software used in the simulations is publicly available online, and all the experiments are reproducible." @default.
- W4384696501 created "2023-07-20" @default.
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- W4384696501 date "2023-07-18" @default.
- W4384696501 modified "2023-10-03" @default.
- W4384696501 title "Preconditioned Infinite GMRES for Parameterized Linear Systems" @default.
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- W4384696501 doi "https://doi.org/10.1137/22m1502380" @default.
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