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Two-Step Modulus-Based Synchronous Multisplitting Iteration Methods for Linear Complementarity Problems

Two-Step Modulus-Based Synchronous Multisplitting Iteration Methods for Linear Complementarity Problems
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Year:    2015

Author:    Lili Zhang

Journal of Computational Mathematics, Vol. 33 (2015), Iss. 1 : pp. 100–112

Abstract

To reduce the communication among processors and improve the computing time for solving linear complementarity problems, we present a two-step modulus-based synchronous multisplitting iteration method and the corresponding symmetric modulus-based multisplitting relaxation methods. The convergence theorems are established when the system matrix is an $H_+$-matrix, which improve the existing convergence theory. Numerical results show that the symmetric modulus-based multisplitting relaxation methods are effective in actual implementation.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1403-m4195

Journal of Computational Mathematics, Vol. 33 (2015), Iss. 1 : pp. 100–112

Published online:    2015-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    13

Keywords:    Linear complementarity problem Modulus-based method Matrix multisplitting Convergence.

Author Details

Lili Zhang

  1. A preconditioned general two-step modulus-based accelerated overrelaxation iteration method for nonlinear complementarity problems

    Zhang, Jia-Lin | Zhang, Guo-Feng | Liang, Zhao-Zheng

    Japan Journal of Industrial and Applied Mathematics, Vol. 39 (2022), Iss. 1 P.227

    https://doi.org/10.1007/s13160-021-00486-8 [Citations: 0]

  2. On perturbation bounds of the linear complementarity problem

    Zheng, Hua | Vong, Seakweng | Li, Wen

    Linear and Multilinear Algebra, Vol. 66 (2018), Iss. 3 P.625

    https://doi.org/10.1080/03081087.2017.1312682 [Citations: 2]

  3. The double-relaxation modulus-based matrix splitting iteration method for linear complementarity problems

    Huang, Zhengge | Cui, Jingjing

    Journal of Computational and Applied Mathematics, Vol. 427 (2023), Iss. P.115138

    https://doi.org/10.1016/j.cam.2023.115138 [Citations: 3]

  4. A modified modulus-based multigrid method for linear complementarity problems arising from free boundary problems

    Zhang, Li-Li | Ren, Zhi-Ru

    Applied Numerical Mathematics, Vol. 164 (2021), Iss. P.89

    https://doi.org/10.1016/j.apnum.2020.09.008 [Citations: 6]

  5. The modulus-based nonsmooth Newton’s method for solving a class of nonlinear complementarity problems of P-matrices

    Zheng, Hua | Vong, Seakweng

    Calcolo, Vol. 55 (2018), Iss. 3

    https://doi.org/10.1007/s10092-018-0279-y [Citations: 13]

  6. Improved convergence theorems of the two-step modulus-based matrix splitting and synchronous multisplitting iteration methods for solving linear complementarity problems

    Zheng, Hua | Vong, Seakweng

    Linear and Multilinear Algebra, Vol. 67 (2019), Iss. 9 P.1773

    https://doi.org/10.1080/03081087.2018.1470602 [Citations: 23]

  7. On the two-stage multisplitting iteration methods for linear complementarity problems

    Guo, Wenxiu | Zheng, Hua | Lu, Xiaoping | Zhang, Yongxiong

    Applied Mathematics and Computation, Vol. 475 (2024), Iss. P.128741

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  8. A relaxed two-step modulus-based matrix synchronous multisplitting iteration method for linear complementarity problems

    Zhang, Yongxiong | Guo, Wenxiu | Zheng, Hua | Vong, Seakweng

    Computational and Applied Mathematics, Vol. 43 (2024), Iss. 1

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    Zhang, Yongxiong | Zheng, Hua | Lu, Xiaoping | Vong, Seakweng

    Applied Mathematics and Computation, Vol. 458 (2023), Iss. P.128248

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  10. A Two-Step Modulus-Based Matrix Splitting Iteration Method Without Auxiliary Variables for Solving Vertical Linear Complementarity Problems

    Zheng, Hua | Lu, Xiaoping | Vong, Seakweng

    Communications on Applied Mathematics and Computation, Vol. 6 (2024), Iss. 4 P.2475

    https://doi.org/10.1007/s42967-023-00280-y [Citations: 4]

  11. Accelerated Relaxation Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems

    Huang, Zheng-Ge | Cui, Jing-Jing

    Bulletin of the Malaysian Mathematical Sciences Society, Vol. 44 (2021), Iss. 4 P.2175

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  12. Modulus-based synchronous multisplitting iteration methods for large sparse vertical linear complementarity problems

    Zheng, Hua | Zhang, Yongxiong | Lu, Xiaoping | Vong, Seakweng

    Numerical Algorithms, Vol. 93 (2023), Iss. 2 P.711

    https://doi.org/10.1007/s11075-022-01436-2 [Citations: 9]

  13. An iteration method for nonlinear complementarity problems

    Zheng, Hua | Li, Wen | Vong, Seakweng

    Journal of Computational and Applied Mathematics, Vol. 372 (2020), Iss. P.112681

    https://doi.org/10.1016/j.cam.2019.112681 [Citations: 4]

  14. Newton-type methods for solving quasi-complementarity problems via sign-based equation

    Zheng, Hua | Vong, Seakweng | Guo, Wen-Xiu

    Calcolo, Vol. 56 (2019), Iss. 2

    https://doi.org/10.1007/s10092-019-0315-6 [Citations: 3]

  15. A preconditioned general two-step modulus-based matrix splitting iteration method for linear complementarity problems of H+-matrices

    Ren, Huan | Wang, Xiang | Tang, Xiao-Bin | Wang, Teng

    Numerical Algorithms, Vol. 82 (2019), Iss. 3 P.969

    https://doi.org/10.1007/s11075-018-0637-5 [Citations: 12]

  16. A two-step modulus-based matrix splitting iteration method for solving nonlinear complementarity problems of $$H_+$$ H + -matrices

    Zheng, Hua | Liu, Ling

    Computational and Applied Mathematics, Vol. 37 (2018), Iss. 4 P.5410

    https://doi.org/10.1007/s40314-018-0646-y [Citations: 16]

  17. A relaxation general two-sweep modulus-based matrix splitting iteration method for solving linear complementarity problems

    Li, Dong-Kai | Wang, Li | Liu, Yu-Ying

    Journal of Computational and Applied Mathematics, Vol. 409 (2022), Iss. P.114140

    https://doi.org/10.1016/j.cam.2022.114140 [Citations: 4]

  18. A two-step iteration method for the horizontal nonlinear complementarity problem

    Zheng, Hua | Luo, Liang | Li, Shao-Yong

    Japan Journal of Industrial and Applied Mathematics, Vol. 38 (2021), Iss. 3 P.1023

    https://doi.org/10.1007/s13160-021-00466-y [Citations: 6]

  19. A class of modified modulus-based synchronous multisplitting iteration methods for linear complementarity problems

    Xu, Weiwei | Zhu, Lei | Peng, Xiaofei | Liu, Hao | Yin, Junfeng

    Numerical Algorithms, Vol. 85 (2020), Iss. 1 P.1

    https://doi.org/10.1007/s11075-019-00799-3 [Citations: 21]

  20. A modified modulus-based matrix splitting iteration method for solving implicit complementarity problems

    Zheng, Hua | Vong, Seakweng

    Numerical Algorithms, Vol. 82 (2019), Iss. 2 P.573

    https://doi.org/10.1007/s11075-018-0614-z [Citations: 28]

  21. The Relaxation Modulus-Based Matrix Splitting Iteration Method for Horizontal Linear Complementarity Problems

    Huang, Zheng-Ge | Cui, Jing-Jing

    Bulletin of the Iranian Mathematical Society, Vol. 48 (2022), Iss. 6 P.3285

    https://doi.org/10.1007/s41980-022-00695-y [Citations: 3]

  22. Accelerated double-relaxation modulus-based matrix splitting iteration method for linear complementarity problems

    Huang, Zhengge | Cui, Jingjing

    Results in Applied Mathematics, Vol. 15 (2022), Iss. P.100304

    https://doi.org/10.1016/j.rinam.2022.100304 [Citations: 4]

  23. A modulus-based multigrid method for nonlinear complementarity problems with application to free boundary problems with nonlinear source terms

    Zhang, Li-Li

    Applied Mathematics and Computation, Vol. 399 (2021), Iss. P.126015

    https://doi.org/10.1016/j.amc.2021.126015 [Citations: 1]

  24. Improved convergence theorems of modulus-based matrix splitting iteration method for nonlinear complementarity problems of H-matrices

    Zheng, Hua

    Calcolo, Vol. 54 (2017), Iss. 4 P.1481

    https://doi.org/10.1007/s10092-017-0236-1 [Citations: 16]

  25. The general two-sweep modulus-based matrix splitting iteration method for solving linear complementarity problems

    Ren, Huan | Wang, Xiang | Tang, Xiao-Bin | Wang, Teng

    Computers & Mathematics with Applications, Vol. 77 (2019), Iss. 4 P.1071

    https://doi.org/10.1016/j.camwa.2018.10.040 [Citations: 26]

  26. Synchronous and Asynchronous Multisplitting Iteration Schemes for Solving Mixed Linear Complementarity Problems with H-Matrices

    Liu, Cuiyu | Li, Chenliang

    Journal of Optimization Theory and Applications, Vol. 171 (2016), Iss. 1 P.169

    https://doi.org/10.1007/s10957-016-0944-8 [Citations: 4]

  27. New convergence proofs of modulus-based synchronous multisplitting iteration methods for linear complementarity problems

    Zhang, Li-Li | Zhang, Yun-Peng | Ren, Zhi-Ru

    Linear Algebra and its Applications, Vol. 481 (2015), Iss. P.83

    https://doi.org/10.1016/j.laa.2015.04.029 [Citations: 9]

  28. Modulus-based synchronous multisplitting method for horizontal nonlinear complementarity problem

    Bu, Fan | Vong, Seakweng | Zheng, Hua

    Journal of Applied Mathematics and Computing, Vol. 70 (2024), Iss. 3 P.2405

    https://doi.org/10.1007/s12190-024-02059-7 [Citations: 0]

  29. The Sign-Based Methods for Solving a Class of Nonlinear Complementarity Problems

    Zheng, Hua | Liu, Ling

    Journal of Optimization Theory and Applications, Vol. 180 (2019), Iss. 2 P.480

    https://doi.org/10.1007/s10957-018-1361-y [Citations: 11]

  30. Improvement of Convergence of One- and Two-Step MSM Iteration Methods for Nondifferentiable Nonlinear Complementarity Problems

    Yan, Gui-Lin | Wu, Yu-Jiang | Deng, Bo

    Communications on Applied Mathematics and Computation, Vol. (2024), Iss.

    https://doi.org/10.1007/s42967-024-00378-x [Citations: 0]

  31. The relaxation modulus-based matrix splitting iteration method for solving a class of nonlinear complementarity problems

    Zheng, Hua | Vong, Seakweng | Liu, Ling

    International Journal of Computer Mathematics, Vol. 96 (2019), Iss. 8 P.1648

    https://doi.org/10.1080/00207160.2018.1504928 [Citations: 19]

  32. The solution of the linear complementarity problem by the matrix analogue of the accelerated overrelaxation iterative method

    Hadjidimos, Apostolos | Tzoumas, Michael

    Numerical Algorithms, Vol. 73 (2016), Iss. 3 P.665

    https://doi.org/10.1007/s11075-016-0112-0 [Citations: 11]

  33. A Two-Step Iteration Method for Vertical Linear Complementarity Problems

    Song, Yunlin | Zheng, Hua | Lu, Xiaoping | Vong, Seak-Weng

    Symmetry, Vol. 14 (2022), Iss. 9 P.1882

    https://doi.org/10.3390/sym14091882 [Citations: 5]

  34. On the convergence of modulus-based matrix splitting iteration methods for a class of nonlinear complementarity problems with H+-matrices

    Li, Rui | Yin, Jun-Feng

    Journal of Computational and Applied Mathematics, Vol. 342 (2018), Iss. P.202

    https://doi.org/10.1016/j.cam.2017.12.029 [Citations: 15]

  35. A relaxation two-step parallel modulus method without auxiliary variable for solving large sparse vertical linear complementarity problems

    Guo, Wenxiu | Zheng, Hua | Lu, Xiaoping | Zhang, Yongxiong | Vong, Seakweng

    Numerical Algorithms, Vol. (2024), Iss.

    https://doi.org/10.1007/s11075-024-01800-4 [Citations: 0]

  36. Comparison of three classes of algorithms for the solution of the linear complementarity problem with an H+-matrix

    Hadjidimos, Apostolos | Zhang, Li-Li

    Journal of Computational and Applied Mathematics, Vol. 336 (2018), Iss. P.175

    https://doi.org/10.1016/j.cam.2017.12.028 [Citations: 14]

  37. Accelerated Relaxation Two-Sweep Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems

    Huang, Zhengge | Cui, Jingjing

    International Journal of Computational Methods, Vol. 21 (2024), Iss. 02

    https://doi.org/10.1142/S0219876223500251 [Citations: 1]

  38. A two-step parallel iteration method for large sparse horizontal linear complementarity problems

    Zhang, Yongxiong | Zheng, Hua | Vong, Seakweng | Lu, Xiaoping

    Applied Mathematics and Computation, Vol. 438 (2023), Iss. P.127609

    https://doi.org/10.1016/j.amc.2022.127609 [Citations: 1]

  39. A non-modulus linear method for solving the linear complementarity problem

    Zheng, Hua | Li, Wen | Qu, Wei

    Linear Algebra and its Applications, Vol. 495 (2016), Iss. P.38

    https://doi.org/10.1016/j.laa.2016.01.032 [Citations: 7]

  40. A generalized modulus-based Newton method for solving a class of non-linear complementarity problems with P-matrices

    Li, Rui | Li, Zhi-Lin | Yin, Jun-Feng

    Numerical Algorithms, Vol. 89 (2022), Iss. 2 P.839

    https://doi.org/10.1007/s11075-021-01136-3 [Citations: 0]

  41. A direct preconditioned modulus-based iteration method for solving nonlinear complementarity problems of H-matrices

    Zheng, Hua | Vong, Seakweng | Liu, Ling

    Applied Mathematics and Computation, Vol. 353 (2019), Iss. P.396

    https://doi.org/10.1016/j.amc.2019.02.015 [Citations: 6]

  42. Two-stage iterations based on composite splittings for rectangular linear systems

    Mishra, Nachiketa | Mishra, Debasisha

    Computers & Mathematics with Applications, Vol. 75 (2018), Iss. 8 P.2746

    https://doi.org/10.1016/j.camwa.2018.01.006 [Citations: 8]

  43. A two-step iteration method for solving vertical nonlinear complementarity problems

    Guo, Wenxiu | Lu, Xiaoping | Zheng, Hua

    AIMS Mathematics, Vol. 9 (2024), Iss. 6 P.14358

    https://doi.org/10.3934/math.2024698 [Citations: 0]

  44. Accelerated modulus-based matrix splitting iteration methods for a restricted class of nonlinear complementarity problems

    Li, Rui | Yin, Jun-Feng

    Numerical Algorithms, Vol. 75 (2017), Iss. 2 P.339

    https://doi.org/10.1007/s11075-016-0243-3 [Citations: 31]