Search Advanced

AIMS Mathematics

2020, Volume 5, Issue 5: 5171-5183. doi: 10.3934/math.2020332
Previous Article Next Article
Research article

A special shift splitting iteration method for absolute value equation

  • School of Mathematics, Yunnan Normal University, Kunming, Yunnan, 650500, P. R. China
  • Received: 13 February 2020 Accepted: 09 June 2020 Published: 15 June 2020

  • MSC : 65F10, 90C05, 90C30

  • In this paper, based on the shift splitting (SS) technique, we propose a special SS iteration method for solving the absolute value equation (AVE), which is obtained by reformulating equivalently the AVE as a two-by-two block nonlinear equation. Theoretical analysis shows that the special SS method is absolutely convergent under proper conditions. Numerical experiments are given to demonstrate the feasibility, robustness and effectiveness of the special SS method.

    Citation: ShiLiang Wu, CuiXia Li. A special shift splitting iteration method for absolute value equation[J]. AIMS Mathematics, 2020, 5(5): 5171-5183. doi: 10.3934/math.2020332

    Related Papers:

  • In this paper, based on the shift splitting (SS) technique, we propose a special SS iteration method for solving the absolute value equation (AVE), which is obtained by reformulating equivalently the AVE as a two-by-two block nonlinear equation. Theoretical analysis shows that the special SS method is absolutely convergent under proper conditions. Numerical experiments are given to demonstrate the feasibility, robustness and effectiveness of the special SS method.


    加载中


    [1] J. Rohn, A theorem of the alternatives for the equation Ax + B|x| = b, Linear Multilinear A., 52 (2004), 421-426. doi: 10.1080/0308108042000220686
    [2] O. L. Mangasarian, Absolute value programming, Comput. Optim. Appl., 36 (2007), 43-53. doi: 10.1007/s10589-006-0395-5
    [3] O. L. Mangasarian, R. R. Meyer, Absolute value equations, Linear Algebra Appl., 419 (2006), 359-367. doi: 10.1016/j.laa.2006.05.004
    [4] S. L. Wu, P. Guo, Modulus-based matrix splitting algorithms for the quasi-complementarity problems, Appl. Numer. Math., 132 (2018), 127-137. doi: 10.1016/j.apnum.2018.05.017
    [5] R. W. Cottle, J. S. Pang, R. E. Stone, The Linear Complementarity Problem, Academic, San Diego, 1992.
    [6] J. Rohn, An algorithm for solving the absolute value equations, Electron. J. Linear Al., 18 (2009), 589-599.
    [7] J. Rohn, V. Hooshyarbakhsh, R. Farhadsefat, An iterative method for solving absolute value equations and sufficient conditions for unique solvability, Optim. Lett., 8 (2014), 35-44. doi: 10.1007/s11590-012-0560-y
    [8] M. A. Noor, J. Iqbal, E. Al-Said, Residual iterative method for solving absolute value equations, Abstr. Appl. Anal., 2012 (2012),1-9.
    [9] D. K. Salkuyeh, The Picard-HSS iteration method for absolute value equations, Optim. Lett., 8 (2014), 2191-2202. doi: 10.1007/s11590-014-0727-9
    [10] M. A. Noor, J. Iqbal, K. I. Noor, et al. On an iterative method for solving absolute value equations, Optim. Lett., 6 (2012), 1027-1033. doi: 10.1007/s11590-011-0332-0
    [11] O. L. Mangasarian, A generalized Newton method for absolute value equations, Optim. Lett., 3 (2009), 101-108. doi: 10.1007/s11590-008-0094-5
    [12] O. L. Mangasarian, A hybrid algorithm for solving the absolute value equation, Optim. Lett., 9 (2015), 1469-1474. doi: 10.1007/s11590-015-0893-4
    [13] A. Wang, Y. Cao, J. X. Chen, Modified Newton-type iteration methods for generalized absolute value equations, J. Optimiz. Theory App., 181 (2019), 216-230. doi: 10.1007/s10957-018-1439-6
    [14] Z. Z. Bai, J. F. Yin, Y. F. Su, A shift-splitting preconditioner for non-Hermitian positive definite matrices, J. Comput. Math., 24 (2006), 539-552.
    [15] M. Z. Zhu, G. F. Zhang, Z. Z. Liang, The nonlinear HSS-like iteration method for absolute value equations, arXiv.org:1403.7013v2.
    [16] S. L. Wu, C. X. Li, The unique solution of the absolute value equations, Appl. Math. Lett., 76 (2018), 195-200. doi: 10.1016/j.aml.2017.08.012
    [17] S. L. Wu, T. Z. Huang, X. L. Zhao, A modified SSOR iterative method for augmented systems, J. Comput. Appl. Math., 228 (2009), 424-433. doi: 10.1016/j.cam.2008.10.006
    [18] Y. F. Ke, C. F. Ma, SOR-like iteration method for solving absolute value equations, Appl. Math. Comput., 311 (2017), 195-202.
    [19] G. H. Golub, X. Wu, J. Y. Yuan, SOR-like methods for augmented systems, BIT., 41 (2001), 71-85. doi: 10.1023/A:1021965717530
    [20] P. Guo, S. L. Wu, C. X. Li, On the SOR-like iteration method for solving absolute value equations, Appl. Math. Lett., 97 (2019), 107-113. doi: 10.1016/j.aml.2019.03.033
  • Reader Comments
  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
AIMS Mathematics
1.8 3.4

Metrics

Article views(3937) PDF downloads(292) Cited by(15)

Preview PDF
Download XML
Export Citation
Article outline

Figures and Tables

Tables(9)

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog