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A residual concept for Krylov subspace evaluation of the matrix function
Mike A. Botchev, Leonid A. Knizhnerman, Eugene E. Tyrtyshnikov
An efficient Krylov subspace algorithm for computing actions of the matrix function for large matrices is proposed. This matrix function is widely used in exponential time inte…
An accurate restarting for shift-and-invert Krylov subspaces computing matrix exponential actions of nonsymmetric matrices
M. A. Botchev
An accurate residual--time (AccuRT) restarting for computing matrix exponential actions of nonsymmetric matrices by the shift-and-invert (SAI) Krylov subspace method is proposed. T…
Practical shift choice in the shift-and-invert Krylov subspace evaluations of the matrix exponential
Alexandr Katrutsa, Mike Botchev, Ivan Oseledets
We propose two methods to find a proper shift parameter in the shift-and-invert method for computing matrix exponential matrix-vector products. These methods are useful in the case…
A nested Schur complement solver with mesh-independent convergence for the time domain photonics modeling
Mike A. Botchev
A nested Schur complement solver is proposed for iterative solution of linear systems arising in exponential and implicit time integration of the Maxwell equations with perfectly m…
ART: adaptive residual--time restarting for Krylov subspace matrix exponential evaluations
Mikhail A. Botchev, Leonid A. Knizhnerman
In this paper a new restarting method for Krylov subspace matrix exponential evaluations is proposed. Since our restarting technique essentially employs the residual, some converge…