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A Modified Generalized Newton Method for Absolute Value Equations

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  • Cui-Xia Li

    (Anyang Normal University)

Abstract

In this paper, a modified generalized Newton method is presented to solve absolute value equations, when all the singular values of the system matrix exceed 1. The convergence properties of the proposed method are given.

Suggested Citation

  • Cui-Xia Li, 2016. "A Modified Generalized Newton Method for Absolute Value Equations," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 1055-1059, September.
    • Handle: RePEc:spr:joptap:v:170:y:2016:i:3:d:10.1007_s10957-016-0956-4
    DOI: 10.1007/s10957-016-0956-4
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    References listed on IDEAS

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    1. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
    2. Louis Caccetta & Biao Qu & Guanglu Zhou, 2011. "A globally and quadratically convergent method for absolute value equations," Computational Optimization and Applications, Springer, vol. 48(1), pages 45-58, January.
    3. C. Zhang & Q. J. Wei, 2009. "Global and Finite Convergence of a Generalized Newton Method for Absolute Value Equations," Journal of Optimization Theory and Applications, Springer, vol. 143(2), pages 391-403, November.
    4. Zhang, Jian-Jun, 2015. "The relaxed nonlinear PHSS-like iteration method for absolute value equations," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 266-274.
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    Cited by:

    1. Yuan Liang & Chaoqian Li, 2023. "Modified Picard-like Method for Solving Absolute Value Equations," Mathematics, MDPI, vol. 11(4), pages 1-18, February.
    2. Cuixia Li, 2022. "Sufficient Conditions for the Unique Solution of a New Class of Sylvester-Like Absolute Value Equations," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 676-683, November.
    3. 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.
    4. An Wang & Yang Cao & Jing-Xian Chen, 2019. "Modified Newton-Type Iteration Methods for Generalized Absolute Value Equations," Journal of Optimization Theory and Applications, Springer, vol. 181(1), pages 216-230, April.

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