Single-step triangular splitting iteration method for a class of complex symmetric linear system

TL;DR

This paper introduces a new single-step triangular splitting iteration method for complex symmetric linear systems, demonstrating its convergence, optimal parameters, and superior performance through theoretical analysis and numerical experiments.

Contribution

The paper proposes a novel single-step iteration method based on triangular splitting for complex symmetric systems, with proven convergence and optimal parameters.

Findings

The method converges under certain conditions.

It outperforms SBTS and PSBTS methods.

Numerical results validate theoretical advantages.

Abstract

For solving a class of block two-by-two real linear system, a new single-step iteration method based on triangular splitting scheme is proposed in this paper. Then the convergence properties of this method are carefully investigated. In addition, we determine its optimal iteration parameters and give the corresponding optimal convergence factor. It is worth mentioning that the SSTS iteration method is robust and superior to SBTS and PSBTS iteration methods under suitable conditions. Finally, some numerical experiments are carried out to validate the theoretical results and evaluate this new method.