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AIMS Mathematics

2023, Volume 8, Issue 5: 10558-10578. doi: 10.3934/math.2023536
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Research article

New matrix splitting iteration method for generalized absolute value equations

  • Department of Mathematics, College of Sciences, Northeastern University, Shenyang 110819, China
  • Received: 06 November 2022 Revised: 09 February 2023 Accepted: 17 February 2022 Published: 02 March 2023

  • MSC : 65F10, 90C05, 90C30

  • In this paper, a relaxed Newton-type matrix splitting (RNMS) iteration method is proposed for solving the generalized absolute value equations, which includes the Picard method, the modified Newton-type (MN) iteration method, the shift splitting modified Newton-type (SSMN) iteration method and the Newton-based matrix splitting (NMS) iteration method. We analyze the sufficient convergence conditions of the RNMS method. Lastly, the efficiency of the RNMS method is analyzed by numerical examples involving symmetric and non-symmetric matrices.

    Citation: Wan-Chen Zhao, Xin-Hui Shao. New matrix splitting iteration method for generalized absolute value equations[J]. AIMS Mathematics, 2023, 8(5): 10558-10578. doi: 10.3934/math.2023536

    Related Papers:

  • In this paper, a relaxed Newton-type matrix splitting (RNMS) iteration method is proposed for solving the generalized absolute value equations, which includes the Picard method, the modified Newton-type (MN) iteration method, the shift splitting modified Newton-type (SSMN) iteration method and the Newton-based matrix splitting (NMS) iteration method. We analyze the sufficient convergence conditions of the RNMS method. Lastly, the efficiency of the RNMS method is analyzed by numerical examples involving symmetric and non-symmetric matrices.


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