On Shift-splitting Based C-to-R Method for Singular Complex Linear Systems.

Rewriting the complex-valued system to realvalued form (C-to-R) leads to a block two-by-two linear system of particular form. Axelsson et al. [Numer. Algorithm 66(2014)811-841] proposed the C-to-R method for nonsingular complex linear systems and illustrated its efficiency theoretically and experimentally. In this paper, we will use the C-to- R method for solving the singular symmetric complex linear systems based on the shift splitting (SS) and obtain an SSbased C-to-R (SS-C-to-R) method. Eigenvalue properties of the SS-C-to-R preconditioned matrix are analyzed. Numerical experiments are also used to demonstrate the feasibility and effectiveness by comparing with the existing preconditioned methods. [ABSTRACT FROM AUTHOR]