Convergence analysis for modified PAHSS-PU method with new parameter setting

Abstract

Based on the modified preconditioned accelerated Hermitian and skew-Hermitian splitting (MPAHSS) and triangular splitting iterative (TSI) methods, this paper presents a new parameter setting to overcome the drawbacks of the MPAHSS-parameterized Uzawa (MPAHSS-PU) method proposed by Huang et al. (J Comput Appl Math 332:1–12, 2018) for sthe saddle point problems. A sufficient condition is provided to ensure the convergence of MPAHSS-PU method with the new parameter setting, and a selection strategy for its parameters is also given. The new parameter setting not only lessens the parameter limitation of the MPAHSS-PU method, but also improves its performance. The validity of the obtained results and the performance of MPAHSS-PU method with the new parameter setting are demonstrated by numerical examples.

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Correspondence to Xing-Bao Gao.

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This work is supported by the National Natural Science Foundation of China under Grant 61273311 and Grant 61502290.

Communicated by Jinyun Yuan.

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Wu, B., Gao, X. Convergence analysis for modified PAHSS-PU method with new parameter setting. Comp. Appl. Math. 39, 196 (2020). https://doi.org/10.1007/s40314-020-01227-2

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Keywords

  • Saddle point problems
  • MPAHSS-PU method
  • New parameter setting
  • Convergence

Mathematics Subject Classification

  • 65F10
  • 65F30
  • 65F50