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Two Efficient Inexact Algorithms for a Class of Large Sparse Complex Linear Systems

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Abstract

Recently Salkuyeh et al. (Int J Comput Math 92:802–815, 2015) studied the generalized SOR (GSOR) iterative method for a class of complex symmetric linear system of equations. In this paper, we present an inexact variant of the GSOR method in which the conjugate gradient and the preconditioned conjugate gradient methods are regarded as its inner iteration processes at each step of the GSOR outer iteration. Moreover, we construct a new method called shifted GSOR iteration method which is obtained from combination of a shift-splitting iteration scheme and the GSOR iteration method. The convergence analysis of the proposed methods are presented. Some numerical experiments are given to show the performance of the methods and are compared with those of the inexact MHSS method.

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Authors and Affiliations

  1. Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran

    Vahid Edalatpour, Davod Hezari & Davod Khojasteh Salkuyeh

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  1. Vahid Edalatpour
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  2. Davod Hezari
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  3. Davod Khojasteh Salkuyeh
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Correspondence to Davod Khojasteh Salkuyeh.

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Edalatpour, V., Hezari, D. & Salkuyeh, D.K. Two Efficient Inexact Algorithms for a Class of Large Sparse Complex Linear Systems. Mediterr. J. Math. 13, 2301–2318 (2016). https://doi.org/10.1007/s00009-015-0621-4

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  • DOI: https://doi.org/10.1007/s00009-015-0621-4

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