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Residual and Restarting in Krylov Subspace Evaluation of the $\varphi$ Function

Year: 2021

Type: article

Abstract: An efficient Krylov subspace algorithm for computing actions of the $\varphi$ matrix 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. We analyze residual convergence and prove, for matrices with numerical range in the stable complex half-plane, that the restarted method is guaranteed to converge for any Krylov subspace dimension. Numerical tests demonstrate efficiency of our approach for solving large scale evolution problems resulting from discretized in space time-dependent PDEs, in particular, diffusion and convection-diffusion problems.

Source: SIAM Journal on Scientific Computing

DOI: 10.1137/20m1375383

Authors: Mike A. Botchev, Leonid Knizhnerman, Eugene E. Tyrtyshnikov

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Ministry of Education and Science of the Russian Federation, Russian Science Foundation

Awards: G2574950007, G2860572879

OpenAlex ID: W3209207841

FWCI: 1.754

Cites: 64

Cited by: 14

Related to: 10