Skip to main content
×
Home
    • Aa
    • Aa
  • Access
  • Cited by 2
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Xie, Shui-Lian Xu, Hong-Ru and Zeng, Jin-Ping 2016. Two-step modulus-based matrix splitting iteration method for a class of nonlinear complementarity problems. Linear Algebra and its Applications, Vol. 494, p. 1.


    Xu, Hongru and Zeng, Jinping 2015. Finite algorithms for the numerical solutions of a class of nonlinear complementarity problems. Journal of Inequalities and Applications, Vol. 2015, Issue. 1,


    ×
  • Bulletin of the Australian Mathematical Society, Volume 82, Issue 3
  • December 2010, pp. 353-366

A MULTIPLICATIVE SCHWARZ ALGORITHM FOR THE NONLINEAR COMPLEMENTARITY PROBLEM WITH AN M-FUNCTION

  • YINGJUN JIANG (a1) and JINPING ZENG (a2)
  • DOI: http://dx.doi.org/10.1017/S0004972710000389
  • Published online: 01 August 2010
Abstract
Abstract

A multiplicative Schwarz iteration algorithm is presented for solving the finite-dimensional nonlinear complementarity problem with an M-function. The monotone convergence of the iteration algorithm is obtained with special choices of initial values. Moreover, by applying the concept of weak regular splitting, the weighted max-norm bound is derived for the iteration errors.

    • Send article to Kindle

      To send this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      A MULTIPLICATIVE SCHWARZ ALGORITHM FOR THE NONLINEAR COMPLEMENTARITY PROBLEM WITH AN M-FUNCTION
      Your Kindle email address
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      A MULTIPLICATIVE SCHWARZ ALGORITHM FOR THE NONLINEAR COMPLEMENTARITY PROBLEM WITH AN M-FUNCTION
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      A MULTIPLICATIVE SCHWARZ ALGORITHM FOR THE NONLINEAR COMPLEMENTARITY PROBLEM WITH AN M-FUNCTION
      Available formats
      ×
Copyright
Corresponding author
For correspondence; e-mail: zengjp@dgut.edu.cn
Footnotes
Hide All

This work is supported by the National Natural Science Foundation of China (Grants 10901027, 10971058).

Footnotes
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]L. Bedea , ‘On the Schwarz alternating method with more than two subdomains for nonlinear monotone problems’, SIAM J. Numer. Anal. 28 (1991), 179204.

[2]M. Benzi , A. Frommer and R. Nabben , ‘Algebraic theory of multiplicative Schwarz methods’, Numer. Math. 89 (2001), 605639.

[4]K.-H. Hoffmann and J. Zou , ‘Parallel solution of variational inequality problems with nonlinear source terms’, IMA J. Numer. Anal. 16 (1996), 3145.

[5]R. H. W. Hoppe , ‘Multigrid algorithms for variational inequalities’, SIAM J. Numer. Anal. 24 (1987), 10461065.

[7]G. Isac , Complementarity Problems (Springer, Berlin, 1992).

[9]Y. Kuznetsov , P. Neittaanmäki and P. Tarvainen , ‘Overlapping domain decomposition methods for the obstacle problem’, in: Domain Decomposition Methods in Science and Engineering, (eds. Y. Kuznetsov , J. Peraux , A. Quarteroni and O. Widlund ) (American Mathematical Society, Providence, RI, 1994), pp. 271277.

[15]Z. Q. Luo and P. Tseng , ‘Error bound and convergence analysis of matrix splitting algorithms for the affine variational inequality problem’, SIAM J. Optim. 2 (1992), 4354.

[16]N. Machida , M. Fukushima and T. Ibaraki , ‘A multisplitting method for symmetric linear complementarity problems’, J. Comput. Appl. Math. 62 (1995), 217227.

[17]J. Moré and W. C. Rheinboldt , ‘On P- and S-functions and related class of n-dimensional nonlinear mappings’, Linear Algebra Appl. 6 (1973), 4568.

[19]F. Scarpini , ‘The alternative Schwarz method applied to some biharmonic variational inequalities’, Calcolo 27 (1990), 5772.

[24]J. P. Zeng , D. H. Li and M. Fukushima , ‘Weighted max-norm estimate of additive Schwarz iteration algorithm for solving linear complementarity problems’, J. Comput. Appl. Math. 131 (2001), 114.

[25]J. P. Zeng and S. Z. Zhou , ‘On monotone and geometric convergence of Schwarz methods for two-sided obstacle problems’, SIAM J. Numer. Anal. 35 (1998), 600616.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords: