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Improved CRI iteration methods for a class of complex symmetric linear systems

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Abstract

For solving a class of complex symmetric linear systems, we improve the combination method of real part and imaginary part (CRI) by introducing two optimization techniques—minimum residual and block successive overrelaxation acceleration—and obtain two new iteration methods: minimum residual CRI (MRCRI) and modified CRI (MCRI). Theoretical analysis implies that the new methods are convergent under suitable conditions. Numerical experiments are used to confirm the effectiveness of the MRCRI and MCRI methods, and experiments of parameter sensitivity show that the MRCRI method is more effective than the CRI and PMHSS methods.

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Funding

This work is supported by National Nature Science Foundation of China with No. 12061048 and Nature Science Foundation of Jiangxi Province with No. 20181ACB20001.

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Authors and Affiliations

  1. College of Mathematics and Computer, Xinyu University, 2666 Sunshine Avenue, Xinyu, 338004, China

    Xiao-Yong Xiao

  2. Department of Mathematics, School of Science, Nanchang University, 999 Xuefu Road, Nanchang, 330031, China

    Xin Qi

  3. Department of Mathematics, College of Liberal Arts and Sciences, University of Illinois Urbana-Champaign, 506 S. Wright St., Urbana, IL, 61801, USA

    Yi-Chao Zhao

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  1. Xiao-Yong Xiao
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  2. Xin Qi
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  3. Yi-Chao Zhao
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Correspondence to Xiao-Yong Xiao.

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Xiao, XY., Qi, X. & Zhao, YC. Improved CRI iteration methods for a class of complex symmetric linear systems. Calcolo 59, 20 (2022). https://doi.org/10.1007/s10092-022-00465-6

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  • DOI: https://doi.org/10.1007/s10092-022-00465-6

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