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Keldysh Institute preprints, 2019, 127, 28 pp. (Mi ipmp2765)  

Adaptive residual-time restarting for Krylov subspace matrix exponential evaluations

M. A. Botchev, L. A. Knizhnerman


Abstract: In this paper a new restarting method for Krylov subspace matrix exponential evaluations is proposed. Since our restarting technique essentially employs the residual, some convergence results for the residual are given. We also discuss how the restart length can be adjusted after each restart cycle, which leads to an adaptive restarting procedure. Numerical tests are presented to compare our restarting with three other restarting methods. Some of the algorithms described in this paper are a part of the Octave/Matlab package expmARPACK available at http://team.kiam.ru/botchev/expm/.

Keywords: Krylov subspace methods, exponential time integration, Arnoldi method, Krylov subspace restarting, shift-and-invert Krylov subspace methods.

DOI: https://doi.org/10.20948/prepr-2019-127

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Citation: M. A. Botchev, L. A. Knizhnerman, “Adaptive residual-time restarting for Krylov subspace matrix exponential evaluations”, Keldysh Institute preprints, 2019, 127, 28 pp.

Citation in format AMSBIB
\Bibitem{BotKni19}
\by M.~A.~Botchev, L.~A.~Knizhnerman
\paper Adaptive residual-time restarting for Krylov subspace matrix exponential evaluations
\jour Keldysh Institute preprints
\yr 2019
\papernumber 127
\totalpages 28
\mathnet{http://mi.mathnet.ru/ipmp2765}
\crossref{https://doi.org/10.20948/prepr-2019-127}


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