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Numerical Algorithms

, Volume 78, Issue 2, pp 643–660 | Cite as

A new single-step iteration method for solving complex symmetric linear systems

  • X. Y. Xiao
  • X. Wang
Original Paper

Abstract

For solving a class of complex symmetric linear systems, we introduce a new single-step iteration method, which can be taken as a fixed-point iteration adding the asymptotical error (FPAE). In order to accelerate the convergence, we further develop the parameterized variant of the FPAE (PFPAE) iteration method. Each iteration of the FPAE and the PFPAE methods requires the solution of only one linear system with a real symmetric positive definite coefficient matrix. Under suitable conditions, we derive the spectral radius of the FPAE and the PFPAE iteration matrices, and discuss the quasi-optimal parameters which minimize the above spectral radius. Numerical tests support the contention that the PFPAE iteration method has comparable advantage over some other commonly used iteration methods, particularly when the experimental optimal parameters are not used.

Keywords

Complex linear system Positive definite HSS iteration Spectral radius Convergence analysis 

Mathematics subject classification (2010)

65F10 65F50 

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of MathematicsSchool of Sciences, Nanchang UniversityNanchangChina
  2. 2.Numerical Simulation and High-Performance Computing LaboratorySchool of Sciences, Nanchang UniversityNanchangChina

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