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AIMS Mathematics

2021, Volume 6, Issue 2: 1258-1275. doi: 10.3934/math.2021078
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Research article

A relaxed generalized Newton iteration method for generalized absolute value equations

  • School of Transportation and Civil Engineering, Nantong University, Nantong, 226019, P. R. China
  • Received: 02 September 2020 Accepted: 10 November 2020 Published: 12 November 2020

  • MSC : 65F10

  • To avoid singular generalized Jacobian matrix and further accelerate the convergence of the generalized Newton (GN) iteration method for solving generalized absolute value equations Ax - B|x| = b, in this paper we propose a new relaxed generalized Newton (RGN) iteration method by introducing a relaxation iteration parameter. The new RGN iteration method involves the well-known GN iteration method and the Picard iteration method as special cases. Theoretical analyses show that the RGN iteration method is well defined and globally linearly convergent under suitable conditions. In addition, a specific sufficient condition is studied when the coefficient matrix A is symmetric positive definite. Finally, two numerical experiments arising from the linear complementarity problems are used to illustrate the effectiveness of the new RGN iteration method.

    Citation: Yang Cao, Quan Shi, Sen-Lai Zhu. A relaxed generalized Newton iteration method for generalized absolute value equations[J]. AIMS Mathematics, 2021, 6(2): 1258-1275. doi: 10.3934/math.2021078

    Related Papers:

  • To avoid singular generalized Jacobian matrix and further accelerate the convergence of the generalized Newton (GN) iteration method for solving generalized absolute value equations Ax - B|x| = b, in this paper we propose a new relaxed generalized Newton (RGN) iteration method by introducing a relaxation iteration parameter. The new RGN iteration method involves the well-known GN iteration method and the Picard iteration method as special cases. Theoretical analyses show that the RGN iteration method is well defined and globally linearly convergent under suitable conditions. In addition, a specific sufficient condition is studied when the coefficient matrix A is symmetric positive definite. Finally, two numerical experiments arising from the linear complementarity problems are used to illustrate the effectiveness of the new RGN iteration method.


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