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AIMS Mathematics

2021, Volume 6, Issue 2: 1743-1753. doi: 10.3934/math.2021104
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Research article

On Picard-SHSS iteration method for absolute value equation

  • College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, PR China
  • Received: 23 September 2020 Accepted: 22 November 2020 Published: 30 November 2020

  • MSC : 65H10, 47H10

  • Picard-type methods are efficient methods for solving the absolute value equation $ Ax-|x| = b $. To further improve the performance of Picard iteration method, a new inexact Picard iteration method, named Picard-SHSS iteration method, is proposed to solve the absolute value equation. The sufficient condition for the convergence of the proposed method for solving the absolute value equation is given. A numerical example is given to demonstrate the effectiveness of the new method.

    Citation: Shu-Xin Miao, Xiang-Tuan Xiong, Jin Wen. On Picard-SHSS iteration method for absolute value equation[J]. AIMS Mathematics, 2021, 6(2): 1743-1753. doi: 10.3934/math.2021104

    Related Papers:

  • Picard-type methods are efficient methods for solving the absolute value equation $ Ax-|x| = b $. To further improve the performance of Picard iteration method, a new inexact Picard iteration method, named Picard-SHSS iteration method, is proposed to solve the absolute value equation. The sufficient condition for the convergence of the proposed method for solving the absolute value equation is given. A numerical example is given to demonstrate the effectiveness of the new method.


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