The generalized C-to-R method for solving complex symmetric indefinite linear systems

Abstract

Recently, Axelsson et al. proposed the so called C-to-R method to solve the complex symmetric definite linear systems (see Axelsson et al., Numer Algor. 2014;66:811–841). In this paper, a generalized C-to-R (GCTR) iterative method is presented for solving the complex symmetric indefinite linear system. The convergent analysis of GCTR method is given, which shows the GCTR method is convergent under the assumptions of $\alpha \ge \frac{\sqrt{2}}{2}$ and has smaller convergence factor than some existing methods. This GCTR method also can result in an efficient preconditioner, which also has tighter clustering than some existing preconditioners. Numerical results are presented, which show full robustness and effectiveness of our proposed method.

Keywords:

• C-to-R method
• iterative method
• complex indefinite linear system
• spectral radius
• preconditioner

AMS Subject Classifications:

• 65F10
• 65N20
• 65F50
• 65N22

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11771193]; the Fundamental Research Funds for the Central Universities [number lzujbky-2017-it56].