On the NPHSS-KPIK iteration method for low-rank complex Sylvester equations arising from time-periodic fractional diffusion equations

Authors: MIN-LI ZENG, GUO-FENG ZHANG

Abstract: Based on the Hermitian and skew-Hermitian (HS) splitting for non-Hermitian matrices, a nonalternating preconditioned Hermitian and skew-Hermitian splitting-Krylov plus inverted Krylov subspace (NPHSS-KPIK) iteration method for solving a class of large and low-rank complex Sylvester equations arising from the two-dimensional time-periodic fractional diffusion problem is established. The local convergence condition is proposed and the optimal parameter is given. Numerical experiments are used to show the efficiency of the NPHSS-KPIK iteration method for solving the Sylvester equations arising from the time-periodic fractional diffusion equations.

Keywords: Sylvester equation, Krylov-plus-inverted-Krylov subspace method, time-periodic fractional diffusion equation, NPHSS method, low-rank

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