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AIMS Mathematics

2022, Volume 7, Issue 5: 8176-8187. doi: 10.3934/math.2022455
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Research article

Two new generalized iteration methods for solving absolute value equations using $ M $-matrix

  • 1.
    School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha 410083, Hunan, China
  • 2.
    Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia
  • 3.
    Research Centre, Future University in Egypt, New Cairo 11745, Egypt
  • Received: 19 October 2021 Revised: 24 January 2022 Accepted: 06 February 2022 Published: 25 February 2022

  • MSC : 90C30, 65F10

  • In this paper, we present two new generalized Gauss-Seidel iteration methods for solving absolute value equations $ Ax-| x | = b, $ where $ A $ is an $ M $-matrix. Furthermore, we demonstrate their convergence under specific assumptions. Numerical tests indicate the efficiency of the suggested methods with suitable parameters.

    Citation: Rashid Ali, Ilyas Khan, Asad Ali, Abdullah Mohamed. Two new generalized iteration methods for solving absolute value equations using $ M $-matrix[J]. AIMS Mathematics, 2022, 7(5): 8176-8187. doi: 10.3934/math.2022455

    Related Papers:

  • In this paper, we present two new generalized Gauss-Seidel iteration methods for solving absolute value equations $ Ax-| x | = b, $ where $ A $ is an $ M $-matrix. Furthermore, we demonstrate their convergence under specific assumptions. Numerical tests indicate the efficiency of the suggested methods with suitable parameters.


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