Two lopsided TSCSP (LTSCSP) iteration methods for solution of complex symmetric positive definite linear systems

In this paper we make two new lopsided methods (LTSCSP1 and LTSCSP2) based on the two-scale-splitting (TSCSP) method and show that the convergence speed of TSCSP iteration method can be increased under some conditions without adding any additional parameter. The convergence analysis of the new methods in detail is given. Then we will obtain the quasi-optimal parameter to minimize the spectral radius of iteration matrix for the new methods. The inexact version of these methods is derived. To illustrate the effectiveness of the proposed framework, several numerical examples are given.

Automated summary

In this paper, we propose two new lopsided methods based on the two-scale-splitting method, LTSCSP1 and LTSCSP2, which can increase the convergence speed of the TSCSP iteration method without adding any additional parameters under certain conditions. The convergence analysis and quasi-optimal parameter determination for the new methods are provided. Additionally, numerical examples are presented to demonstrate the effectiveness of the proposed framework.