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On the minimum convergence factor of a class of GSOR-like methods for augmented systems

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Abstract

This study proposes a class of GSOR-like methods with two real functions. Based on previously used assumptions, the convergence of each method in the class is analyzed and the minimum convergence factor of the methods in the class is estimated. We show that the GSOR-like methods reported in the past decade are equivalent and all of their optimal convergence factors reach the minimum. Contour maps are drawn to show the behaviors of the convergence factors of these methods near the optimum parameters.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, People’s Republic of China

    Zhengda Huang & Xiaoyan Zhou

  2. School of Sciences, Zhejiang University of Science and Technology, Hangzhou, 310023, People’s Republic of China

    Xiaoyan Zhou

Authors
  1. Zhengda Huang
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  2. Xiaoyan Zhou
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Corresponding author

Correspondence to Zhengda Huang.

Additional information

This research is supported by the ZPNSFC (Grant No. LY12A01023) and partly supported by the NSFC(Grant No. 11471285).

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Huang, Z., Zhou, X. On the minimum convergence factor of a class of GSOR-like methods for augmented systems. Numer Algor 70, 113–132 (2015). https://doi.org/10.1007/s11075-014-9937-6

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  • DOI: https://doi.org/10.1007/s11075-014-9937-6

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