Accelerated PMHSS iteration methods for complex symmetric linear systems

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• 作者：Qing-Qing Zheng ; Chang-Feng Ma
• 关键词：Complex symmetric linear system ; PMHSS iteration ; Convergence theory ; Iterative methods ; Accelerated technology
• 刊名：Numerical Algorithms
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：73
• 期：2
• 页码：501-516
• 全文大小：584 KB
• 刊物类别：Computer Science
• 刊物主题：Numeric Computing
  Algorithms
  Mathematics
  Algebra
  Theory of Computation
  
• 出版者：Springer U.S.
• ISSN：1572-9265
• 卷排序：73

文摘

In this paper, we introduce and analyze an accelerated preconditioning modification of the Hermitian and skew-Hermitian splitting (APMHSS) iteration method for solving a broad class of complex symmetric linear systems. This accelerated PMHSS algorithm involves two iteration parameters α,β and two preconditioned matrices whose special choices can recover the known PMHSS (preconditioned modification of the Hermitian and skew-Hermitian splitting) iteration method which includes the MHSS method, as well as yield new ones. The convergence theory of this class of APMHSS iteration methods is established under suitable conditions. Each iteration of this method requires the solution of two linear systems with real symmetric positive definite coefficient matrices. Theoretical analyses show that the upper bound σ₁(α,β) of the asymptotic convergence rate of the APMHSS method is smaller than that of the PMHSS iteration method. This implies that the APMHSS method may converge faster than the PMHSS method. Numerical experiments on a few model problems are presented to illustrate the theoretical results and examine the numerical effectiveness of the new method.