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An accurate residual--time (AccuRT) restarting for computing matrixexponential actions of nonsymmetric matrices by the shift-and-invert (SAI)Krylov subspace method is proposed. The proposed restarting method is anextension of the recently proposed RT (residual--time) restarting and it isdesigned to avoid a possible accuracy loss in the conventional RT restarting.An expensive part of the SAI Krylov method is solution of linear systems withthe shifted matrix. Since the AccuRT algorithm adjusts the shift value, wediscuss how the proposed restarting can be implemented with just a singleLU~factorization (or a preconditioner setup) of the shifted matrix. Numericalexperiments demonstrate an improved accuracy and efficiency of the approach.

An accurate restarting for shift-and-invert Krylov subspaces computing matrix exponential actions of nonsymmetric matrices