Parameterized GSOR Method for a Class of Complex Symmetric Systems of Linear Equations

Authors

  • Yujiang Wu School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, Gansu, P.R. China
  • Wei-Hong Zhang School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, P.R. China
  • Xi-An Li School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, P.R. China
  • Ai-Li Yang School of Mathematics and Statistics/Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, P.R. China

DOI:

https://doi.org/10.4208/jms.v52n1.19.02

Keywords:

Complex linear systems, symmetric positive definite, spectral radius, convergence, preconditioning.

Abstract

A parameterized generalized successive overrelaxation (PGSOR) method for a class of block two-by-two linear system is established in this paper. The convergence theorem of the method is proved under suitable assumptions on iteration parameters. Besides, we obtain a functional equation between the parameters and the eigenvalues of the iteration matrix for this method. Furthermore, an accelerated variant of the PGSOR (APGSOR) method is also presented in order to raise the convergence rate. Finally, numerical experiments are carried out to confirm the theoretical analysis as well as the feasibility and the efficiency of the PGSOR method and its variant.

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Published

2019-03-06

Issue

Vol. 52 No. 1 (2019)

Section

Articles