Search Advanced

AIMS Mathematics

2022, Volume 7, Issue 1: 606-616. doi: 10.3934/math.2022038
Previous Article Next Article
Research article Special Issues

Modified BAS iteration method for absolute value equation

  • 1.
    School of Mathematics, Yunnan Normal University, Kunming, Yunnan 650500, China
  • 2.
    Shaanxi Key Laboratory of Industrial Automation, Shaanxi University of Technology, Hanzhong, Shaanxi 723001, China
  • Received: 14 July 2021 Accepted: 29 September 2021 Published: 14 October 2021

  • MSC : 65F10, 90C05, 90C30

  • In this paper, to improve the convergence speed of the block-diagonal and anti-block-diagonal splitting (BAS) iteration method, we design a modified BAS (MBAS) method to obtain the numerical solution of the absolute value equation. Theoretical analysis shows that under certain conditions the MBAS method is convergent. Numerical experiments show that the MBAS method is feasible.

    Citation: Cui-Xia Li, Long-Quan Yong. Modified BAS iteration method for absolute value equation[J]. AIMS Mathematics, 2022, 7(1): 606-616. doi: 10.3934/math.2022038

    Related Papers:

  • In this paper, to improve the convergence speed of the block-diagonal and anti-block-diagonal splitting (BAS) iteration method, we design a modified BAS (MBAS) method to obtain the numerical solution of the absolute value equation. Theoretical analysis shows that under certain conditions the MBAS method is convergent. Numerical experiments show that the MBAS method is feasible.


    加载中


    [1] C. X. Li, S. L. Wu, Block-diagonal and anti-block-diagonal splitting iteration method for absolute value equation, In: Simulation tools and techniques, 12th EAI International Conference, SIMUtools 2020, Guiyang, China, 369 (2021), 572–581. doi: 0.1007/978-3-030-72792-5_45.
    [2] O. L. Mangasarian, A generalized Newton method for absolute value equations, Optim. Lett., 3 (2009), 101–108. doi: 10.1007/s11590-008-0094-5. doi: 10.1007/s11590-008-0094-5
    [3] Z. Z. Bai, X. Yang, On HSS-based iteration methods for weakly nonlinear systems, Appl. Numer. Math., 59 (2009), 2923–2936. doi: 10.1016/j.apnum.2009.06.005. doi: 10.1016/j.apnum.2009.06.005
    [4] M. Z. Zhu, Y. E. Qi, The nonlinear HSS-like iteration method for absolute value equations, arXiv. Available from: https://arXiv.org/abs/1403.7013v4.
    [5] 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. doi: 10.1080/0308108042000220686
    [6] O. L. Mangasarian, Absolute value programming, Comput. Optim. Applic., 36 (2007), 43–53. doi: 10.1007/s10589-006-0395-5. doi: 10.1007/s10589-006-0395-5
    [7] O. L. Mangasarian, R. R. Meyer, Absolute value equations, Linear Algebra Appl., 419 (2006), 359–367. doi: 10.1016/j.laa.2006.05.004. doi: 10.1016/j.laa.2006.05.004
    [8] 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. doi: 10.1016/j.apnum.2018.05.017
    [9] R. W. Cottle, J. S. Pang, R. E. Stone, The linear complementarity problem, Society for Industrial and Applied Mathematics, 2009. doi: 10.1137/1.9780898719000.
    [10] J. Rohn, An algorithm for solving the absolute value equations, Electron. J. Linear Algebra, 18 (2009), 589–599. doi: 10.13001/1081-3810.1332. doi: 10.13001/1081-3810.1332
    [11] 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. doi: 10.1007/s11590-012-0560-y
    [12] 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. doi: 10.1007/s11590-014-0727-9
    [13] 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. doi: 10.1007/s11590-015-0893-4
    [14] 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. doi: 10.1016/j.cam.2008.10.006
    [15] C. X. Li, S. L. Wu, Modified SOR-like iteration method for absolute value equations, Math. Probl. Eng., 2020 (2020), 9231639. doi: 10.1155/2020/9231639. doi: 10.1155/2020/9231639
    [16] A. X. Wang, H. J. Wang, Y. K. Deng, Interval algorithm for absolute value equations, Cent. Eur. J. Math., 9 (2011), 1171–1184. doi: 10.2478/s11533-011-0067-2. doi: 10.2478/s11533-011-0067-2
    [17] S. Ketabchi, H. Moosaei, An efficient method for optimal correcting of absolute value equations by minimal changes in the right hand side, Comput. Math. Appl., 64 (2012), 1882–1885. doi: 10.1016/j.camwa.2012.03.015. doi: 10.1016/j.camwa.2012.03.015
    [18] C. Zhang, Q. J. Wei, Global and finite convergence of a generalized newton method for absolute value equations, J. Optim. Theory. Appl., 143 (2009), 391–403. doi: 10.1007/s10957-009-9557-9. doi: 10.1007/s10957-009-9557-9
    [19] C. X. Li, A preconditioned AOR iterative method for the absolute value equations, Inter. J. Comput. Meth., 14 (2017), 1750016. doi: 10.1142/S0219876217500165. doi: 10.1142/S0219876217500165
    [20] J. M. Ortega, W. C. Rheinboldt, Iterative solution of nonlinear equations in several variables, Academic Press, 1970. doi: 10.1016/C2013-0-11263-9.
    [21] Y. F. Ke, C. F. Ma, SOR-like iteration method for solving absolute value equations, Appl. Math. Comput., 311 (2017), 195–202. doi: 10.1016/j.amc.2017.05.035. doi: 10.1016/j.amc.2017.05.035
    [22] Y. F. Ke, The new iteration algorithm for absolute value equation, Appl. Math. Lett., 99 (2020), 105990. doi: 10.1016/j.aml.2019.07.021. doi: 10.1016/j.aml.2019.07.021
    [23] T. Saha, S. Srivastava, S. Khare, P. S. Stanimirovic, M. D. Petkovic, An improved algorithm for basis pursuit problem and its applications, Appl. Math. Comput., 355 (2019), 385–398. doi: 10.1016/j.amc.2019.02.073. doi: 10.1016/j.amc.2019.02.073
    [24] M. D. Petkovic, Generalized Schultz iterative methods for the computation of outer inverses, Comput. Math. Appl., 67 (2014), 1837–1847. doi: 10.1016/j.camwa.2014.03.019. doi: 10.1016/j.camwa.2014.03.019
    [25] M. D. Petkovic, M. A. Krstic, K. P. Rajkovic, Rapid generalized Schultz iterative methods for the computation of outer inverses, J. Comput. Appl. Math., 344 (2018), 572–584 doi: 10.1016/j.cam.2018.05.048. doi: 10.1016/j.cam.2018.05.048
    [26] M. Benzi, G. H. Golub, J. Liesen, Numerical solution of saddle point problems, Acta Numer., 14 (2005), 1–137. doi: 10.1017/S0962492904000212. doi: 10.1017/S0962492904000212
    [27] Z. Z. Bai, Z. Q. Wang, On parameterized inexact Uzawa methods for generalized saddle point problems, Linear Algebra Appl., 428 (2008), 2900–2932. doi: 10.1016/j.laa.2008.01.018. doi: 10.1016/j.laa.2008.01.018
  • Reader Comments
  • © 2022 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(2367) PDF downloads(114) Cited by(1)

Preview PDF
Download XML
Export Citation
Article outline

Figures and Tables

Tables(5)

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog