# Two-parameter TSCSP method for solving complex symmetric system of linear equations

## TL;DR

This paper proposes a new two-parameter iterative method, TTSCSP, for efficiently solving complex symmetric linear systems, with convergence analysis, optimal parameters, and numerical comparisons demonstrating its effectiveness.

## Contribution

Introduction of the two-parameter TTSCSP method and its inexact version, including convergence conditions, optimal parameters, and comprehensive numerical comparisons.

## Key findings

- TTSCSP converges under specified conditions.
- Optimal parameters minimize spectral radius.
- Numerical results show TTSCSP outperforms existing methods.

## Abstract

We introduce a two-parameter version of the two-step scale-splitting iteration method, called TTSCSP, for solving a broad class of complex symmetric system of linear equations. We present some conditions for the convergence of the method. An upper bound for the spectral radius of the method is presented and optimal parameters which minimize this bound are given. Inexact version of the TTSCSP iteration method (ITTSCSP) is also presented. Some numerical experiments are reported to verify the effectiveness of the TTSCSP iteration method and the numerical results are compared with those of the TSCSP, the SCSP and the PMHSS iteration methods. Numerical comparison of the ITTSCSP method with the inexact version of TSCSP, SCSP and PMHSS are presented. We also compare the numerical results of the BiCGSTAB method in conjunction with the TTSCSP and the ILU preconditioners.