An iteration method for solving the linear system Ax=b. (15th April 2018)

• Record Type: Journal Article
• Authors: Tian, Zhaolu; Tian, Maoyi; Zhang, Yan; Wen, Pihua
• Is Part Of: Computers & mathematics with applications. Volume 75:issue 8(2018)
• Page Start: 2710
• Page End: 2722
• Publication Date: 2018-04-15
• Subjects: Inner-outer iterations -- Convergence -- Accelerate -- Preconditioned; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2018.01.003
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper, based on a convergence splitting of the matrix A, we present an inner–outer iteration method for solving the linear system A x = b . We analyze the overall convergence of this method without any other restriction on its parameters. Moreover, we give the accelerated inner–outer iteration method, and discuss how to apply the inner–outer iterations as a preconditioner for the Krylov subspace methods. The inner–outer iteration method can also be used for the solution of A X B = C . Finally, several numerical examples are given to validate the performance of our proposed algorithms.