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A generalization of the Gauss–Seidel iteration method for solving absolute value equations

Author

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  • Edalatpour, Vahid
  • Hezari, Davod
  • Khojasteh Salkuyeh, Davod

Abstract

Based on the Gauss–Seidel splitting, we present a new matrix splitting iteration method, called generalized Gauss–Seidel (GGS) iteration method, for solving the large sparse absolute value equation (AVE) Ax−|x|=b where A∈Rn×n and b∈Rn and investigate its convergence properties. Moreover, by preconditioning AVE, a preconditioned variant of the GGS (PGGS) method is presented. Numerical experiments illustrate the efficiency of both GGS and PGGS iterations.

Suggested Citation

  • Edalatpour, Vahid & Hezari, Davod & Khojasteh Salkuyeh, Davod, 2017. "A generalization of the Gauss–Seidel iteration method for solving absolute value equations," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 156-167.
    • Handle: RePEc:eee:apmaco:v:293:y:2017:i:c:p:156-167
    DOI: 10.1016/j.amc.2016.08.020
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    Cited by:

    1. Ke, Yi-Fen & Ma, Chang-Feng, 2017. "SOR-like iteration method for solving absolute value equations," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 195-202.
    2. Peng Guo & Javed Iqbal & Syed Muhammad Ghufran & Muhammad Arif & Reem K. Alhefthi & Lei Shi, 2023. "A New Efficient Method for Absolute Value Equations," Mathematics, MDPI, vol. 11(15), pages 1-9, July.
    3. Francesco Mezzadri & Emanuele Galligani, 2022. "Projected Splitting Methods for Vertical Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 598-620, June.

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