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BIT Numerical Mathematics
Erschienen in: BIT Numerical Mathematics 2/2021

19.01.2021

Inexact rational Krylov method for evolution equations

verfasst von: Yuka Hashimoto, Takashi Nodera

Erschienen in: BIT Numerical Mathematics | Ausgabe 2/2021

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Abstract

Linear and nonlinear evolution equations have been formulated to address problems in various fields of science and technology. Recently, methods using an exponential integrator for solving evolution equations, where matrix functions must be computed repeatedly, have been investigated and refined. In this paper, we propose a new method for computing these matrix functions which is called an inexact rational Krylov method. This is a more efficient version of the rational Krylov method with appropriate shifts, which was proposed by Hashimoto and Nodera (ANZIAM J 58:C149–C161, 2016). The advantage of the inexact rational Krylov method is that it computes linear equations that appear in the rational Krylov method efficiently while guaranteeing the accuracy of the final solution.
Vorheriger Artikel Numerical conservative solutions of the Hunter–Saxton equation
Nächster Artikel Adjoint-based exact Hessian computation

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Metadaten
Titel
Inexact rational Krylov method for evolution equations
verfasst von
Yuka Hashimoto
Takashi Nodera
Publikationsdatum
19.01.2021
Verlag
Springer Netherlands
Erschienen in
BIT Numerical Mathematics / Ausgabe 2/2021
Print ISSN: 0006-3835
Elektronische ISSN: 1572-9125
DOI
https://doi.org/10.1007/s10543-020-00829-w

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