# A residual concept for Krylov subspace evaluation of the $\varphi$ matrix function

@inproceedings{Botchev2020ARC, title={A residual concept for Krylov subspace evaluation of the \$\varphi\$ matrix function}, author={Mike A. Botchev and Leonid A. Knizhnerman and Eugene E. Tyrtyshnikov}, year={2020} }

An efficient Krylov subspace algorithm for computing actions of the φmatrix function for large matrices is proposed. This matrix function is widely used in exponential time integration, Markov chains and network analysis and many other applications. Our algorithm is based on a reliable residual based stopping criterion and a new efficient restarting procedure. For matrices with numerical range in the stable complex half plane, we analyze residual convergence and prove that the restarted method…

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