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- W2018687656 abstract "We consider the approximation of the matrix $varphi$-functions that appear in exponential integrators for stiff systems of differential equations. For stiff systems, the field-of-values of the occurring matrices is large and lies somewhere in the left complex half-plane. In order to obtain an efficient method uniformly for all matrices with a field-of-values in the left complex half-plane, we consider the approximation by a rational Krylov subspace method with equidistant poles of order one on the line $mbox{Re},z = gamma > 0$. We present error bounds that predict a faster convergence rate as for the resolvent Krylov subspace approximation using a single repeated pole at $gamma > 0$. Poles of order one allow moreover for a parallel implementation of the corresponding rational Krylov subspace decomposition. We analyze the convergence of the proposed rational Krylov subspace method and present numerical experiments that illustrate our results." @default.
- W2018687656 created "2016-06-24" @default.
- W2018687656 creator A5058313922 @default.
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- W2018687656 date "2014-01-01" @default.
- W2018687656 modified "2023-09-29" @default.
- W2018687656 title "Uniform Approximation of $varphi$-Functions in Exponential Integrators by a Rational Krylov Subspace Method with Simple Poles" @default.
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- W2018687656 doi "https://doi.org/10.1137/140964655" @default.
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