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Modulus-based Synchronous Multisplitting Iteration Methods for an Implicit Complementarity Problem

  • Chen-Liang Li (a1) and Jun-Tao Hong (a1)
Abstract
Abstract

We construct modulus-based synchronous multisplitting iteration methods to solve a large implicit complementarity problem on parallel multiprocessor systems, and prove their convergence. Numerical results confirm our theoretical analysis and show that these new methods are efficient.

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*Corresponding author. Email address: chenliang_li@hotmail.com (C.-L. Li)
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[1] Z-Z. Bai , The convergence of parallel iteration algorithms for linear complementarity problems, Computers and Mathematics with Applications 32, 117 (1996).

[2] Z-Z. Bai , On the convergence of the multisplitting methods for the linear complementarity problem, SIAM Journal of Matrix Analysis and Applications 21, 6778 (1999).

[3] Z-Z. Bai , Modulus-based matrix splitting iteration methods for linear complementarity problems, Numerical Linear Algebra with Applications 17, 917933 (2010).

[6] Z-Z. Bai , J-C. Sun and D-R. Wang , A unified framework for the construction of various matrix multisplitting iterative methods for large sparse system of linear equations, Computers and Mathematics with Applications 32, 5176 (1996).

[7] Z-Z Bai and L-L. Zhang , Modulus-based synchronous multisplitting iteration methods for linear complementarity problems, Numerical Linear Algebra with Applications 20, 425439 (2013).

[8] Z-Z. Bai and L-L. Zhang , Modulus-based synchronous two-stage multisplitting iteration methods for linear complementarity problems, Numerical Algorithms 62, 5977 (2013).

[10] C.L. Cvetkov and V, Kostic, A note on the convergence of the MSMAOR method for linear complementarity problems, Numerical Linear Algebra with Applications 21, 534539 (2014).

[11] J-L. Dong , Inexact multisplitting methods for linear complementarity problems, Journal of Computational and Applied Mathematics 223, 714724 (2009).

[12] J-L. Dong and M-Q. Jiang , A modified modulus method for symmetric positive-definite linear complementarity problems, Numerical Linear Algebra with Applications 16, 129143 (2009).

[14] A. Frommer and D.B. Szyld , H-splittings and two-stage iterative methods, Numerische Mathematik 63, 345356 (1992).

[15] A. Hadjidimos , M. Lapidakis and M. Tzoumas , On iterative solution for linear complementarity problems with an H+matrix, SIAM Journal of Matrix Analysis and Applications 33, 97110 (2012).

[16] A. Hadjidimos and M. Tzoumas , Nonstationary extrapolated modulus algorithms for the solution of the linear complementarity problem, Linear Algebra and Its Applications 431, 197210 (2009).

[17] J-T. Hong and C-L. Li , Modulus-based matrix splitting iteration methods for a class of implicit complementarity problems, Numerical Linear Algebra with Applications 23, 629641 (2016).

[18] N.W. Kapple and L.T. Waston , Iterative algorithms for the linear complementarity problems, International Journal of Computer Mathematics 19, 273297 (1986).

[19] D.P. O’Leary and R.E. White , Multisplitting of matrices and parallel solution of linear system, SIAM Journal on Algebraic Discrete Methods 6, 630640 (1985).

[22] W Li , A general modulus-based matrix splitting iteration methods for linear complementarity problems of H-matrices, Applied Mathematics Letters 26, 11591164 (2013).

[23] N. Machida , N. Fukushima and T. Ibaraki , A multisplitting method for symmetric linear complementarity problems, Journal of Computational and Applied Mathematics 62, 217227 (1995).

[27] L-L. Zhang , Two-step modulus-based matrix splitting iteration methods for linear complementarity problems, Numerical Algorithms 57, 8399 (2011).

[28] L-L. Zhang , Two-stage multisplitting iteration methods using modulus-based matrix splitting as inner iteration for linear complementarity problems, Journal of Optimization Theory and Applications 160, 189203 (2014).

[30] L-L. Zhang and Z-R. Ren , Improved convergence theorems of modulus-based matrix splitting iteration methods for linear complementarity problems, Applied Mathematics Letters 26, 638642 (2013).

[31] N Zheng and J-F. Yin , Accelerated modulus-based matrix splitting iteration methods for linear complementarity problem, Numerical Algorithms 64, 245262 (2013).

[32] N Zheng and J-F. Yin , Convergence of accelerated modulus-based matrix splitting iteration methods for linear complementarity problem with an H+-matrix, Journal of Computational and Applied Mathematics 260, 281293 (2014).

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East Asian Journal on Applied Mathematics
  • ISSN: 2079-7362
  • EISSN: 2079-7370
  • URL: /core/journals/east-asian-journal-on-applied-mathematics
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