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Original Articles

Matrix Multisplitting Methods with Applications to Linear Complementarity Problems∶ Parallel Asynchronous Methods

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Pages 205-232 | Published online: 15 Sep 2010

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Yu-Jiang Wu, Wei-Hong Zhang & Ai-Li Yang. (2022) Modulus-based inexact non-alternating preconditioned splitting method for linear complementarity problems. Linear and Multilinear Algebra 70:22, pages 7414-7432.
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Lu-Bin Cui, Cui-Xia Li & Shi-Liang Wu. (2021) The relaxation convergence of multisplitting AOR method for linear complementarity problem. Linear and Multilinear Algebra 69:1, pages 40-47.
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Cui-Xia Li. (2021) The improved convergence of MSMMAOR method for linear complementarity problems. Linear and Multilinear Algebra 69:1, pages 1-8.
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Hua Zheng, Seakweng Vong & Ling Liu. (2019) The relaxation modulus-based matrix splitting iteration method for solving a class of nonlinear complementarity problems. International Journal of Computer Mathematics 96:8, pages 1648-1667.
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Shi-Liang Wu & Cui-Xia Li. (2016) A note on the MSMAOR method for linear complementarity problems. Linear and Multilinear Algebra 64:4, pages 795-800.
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Bharat Kumar, Deepmala & Arup K Das. (2023) A note on fixed point method and linear complementarity problem. Journal of Numerical Analysis and Approximation Theory 52:1, pages 82-89.
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Hua Zheng, Yongxiong Zhang, Xiaoping Lu & Seakweng Vong. (2022) Modulus-based synchronous multisplitting iteration methods for large sparse vertical linear complementarity problems. Numerical Algorithms 93:2, pages 711-729.
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Dongmei Yu, Yiming Zhang, Cairong Chen & Deren Han. (2023) A new relaxed acceleration two-sweep modulus-based matrix splitting iteration method for solving linear complementarity problems. AIMS Mathematics 8:6, pages 13368-13389.
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Dongmei Yu, Yifei Yuan & Yiming Zhang. (2023) A preconditioned new modulus-based matrix splitting method for solving linear complementarity problem of $ H_+ $-matrices. Electronic Research Archive 31:1, pages 123-146.
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Mei Feng, Xiang Wang & Teng Wang. (2023) The square-Newton iteration for linear complementarity problem. Filomat 37:2, pages 467-476.
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Litao Zhang, Yifan Zhang, Xiaojing Zhang & Jianfeng Zhao. (2023) A ACCELERATED MODIFIED SHIFT-SPLITTING METHOD FOR NONSYMMETRIC SADDLE POINT PROBLEMS. Journal of Applied Analysis & Computation 13:4, pages 2283-2296.
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Changfeng Ma & Ting Wang. (2023) THE MODULUS-BASED MATRIX SPLITTING METHOD WITH INNER ITERATION FOR A CLASS OF NONLINEAR COMPLEMENTARITY PROBLEMS. Journal of Applied Analysis & Computation 13:2, pages 701-714.
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Chen-Can Zhou, Jie Qiu, Yang Cao, Geng-Chen Yang, Qin-Qin Shen & Quan Shi. (2023) An accelerated modulus-based matrix splitting iteration method for mixed-size cell circuits legalization. Integration 88, pages 20-31.
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Francesco Mezzadri & Emanuele Galligani. (2021) Projected Splitting Methods for Vertical Linear Complementarity Problems. Journal of Optimization Theory and Applications 193:1-3, pages 598-620.
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Chen-Can Zhou, Qin-Qin Shen, Geng-Chen Yang & Quan Shi. (2022) A general modulus-based matrix splitting method for quasi-complementarity problem. AIMS Mathematics 7:6, pages 10994-11014.
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Li-Tao Zhang, Ying-Chao Zhao, Yi-Fan Zhang & Sheng-Kun Li. (2022) RELAXED MODULUS-BASED SYNCHRONOUS MULTISPLITTING MULTI-PARAMETERS TOR (TWO-PARAMETERS OVER-RELAXATION) METHODS FOR LINEAR COMPLEMENTARITY PROBLEMS. Journal of Applied Analysis & Computation 12:4, pages 1403-1417.
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Xianping Wu. (2022) The refined error bounds for linear complementarity problems of -matrices . Journal of Computational and Applied Mathematics 400, pages 113751.
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Jia-Lin Zhang, Guo-Feng Zhang & Zhao-Zheng Liang. (2021) A preconditioned general two-step modulus-based accelerated overrelaxation iteration method for nonlinear complementarity problems. Japan Journal of Industrial and Applied Mathematics 39:1, pages 227-255.
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Zhizhi Li, Huai Zhang & Le Ou-Yang. (2021) The selection of the optimal parameter in the modulus-based matrix splitting algorithm for linear complementarity problems. Computational Optimization and Applications 80:2, pages 617-638.
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Zheng-Ge Huang & Jing-Jing Cui. (2021) Accelerated Relaxation Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems. Bulletin of the Malaysian Mathematical Sciences Society 44:4, pages 2175-2213.
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Li Sun & Yu-Mei Huang. (2021) A modulus-based multigrid method for image retinex. Applied Numerical Mathematics 164, pages 199-210.
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Francesco Mezzadri & Emanuele Galligani. (2020) Modulus-based matrix splitting methods for a class of horizontal nonlinear complementarity problems. Numerical Algorithms 87:2, pages 667-687.
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Li-Tao Zhang, Ding-De Jiang, Xian-Yu Zuo, Ying-Chao Zhao & Yi-Fan Zhang. (2019) Relaxed Modulus-Based Synchronous Multisplitting Multi-Parameter Methods for Linear Complementarity Problems. Mobile Networks and Applications 26:2, pages 745-754.
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Shiliang Wu, Cuixia Li & Praveen Agarwal. (2021) Relaxed Modulus-Based Matrix Splitting Methods for the Linear Complementarity Problem. Symmetry 13:3, pages 503.
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Yifen Ke. (2020) The Matrix Splitting Iteration Method for Nonlinear Complementarity Problems Associated with Second-Order Cone. Bulletin of the Iranian Mathematical Society 47:1, pages 31-53.
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Francesco Mezzadri. (2020) Modulus‐based synchronous multisplitting methods for solving horizontal linear complementarity problems on parallel computers. Numerical Linear Algebra with Applications 27:5.
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Weiwei Xu, Lei Zhu, Xiaofei Peng, Hao Liu & Junfeng Yin. (2019) A class of modified modulus-based synchronous multisplitting iteration methods for linear complementarity problems. Numerical Algorithms 85:1, pages 1-21.
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Litao Zhang & Xianyu Zuo. (2020) GLOBAL RELAXED MODULUS-BASED SYNCHRONOUS BLOCK MULTISPLITTING MULTI-PARAMETERS METHODS FOR LINEAR COMPLEMENTARITY PROBLEMS. Journal of Applied Analysis & Computation 10:4, pages 1267-1281.
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Xi-Ming Fang & Zhi-Wei Zhu. (2019) The modulus-based matrix double splitting iteration method for linear complementarity problems. Computers & Mathematics with Applications 78:11, pages 3633-3643.
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Huan Ren, Xiang Wang, Xiao-Bin Tang & Teng Wang. (2018) A preconditioned general two-step modulus-based matrix splitting iteration method for linear complementarity problems of H+-matrices. Numerical Algorithms 82:3, pages 969-986.
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Min-Hua Wu & Chen-Liang Li. (2019) A preconditioned modulus-based matrix multisplitting block iteration method for the linear complementarity problems with Toeplitz matrix. Calcolo 56:2.
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Huan Ren, Xiang Wang, Xiao-Bin Tang & Teng Wang. (2019) The general two-sweep modulus-based matrix splitting iteration method for solving linear complementarity problems. Computers & Mathematics with Applications 77:4, pages 1071-1081.
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Xue Yang, Yu-Mei Huang & Li Sun. (2018) A modulus iteration method for retinex problem. Numerical Linear Algebra with Applications 25:6, pages e2207.
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Shi-Liang Wu & Peng Guo. (2018) Modulus-based matrix splitting algorithms for the quasi-complementarity problems. Applied Numerical Mathematics 132, pages 127-137.
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Baohua Huang & Changfeng Ma. (2017) Accelerated modulus-based matrix splitting iteration method for a class of nonlinear complementarity problems. Computational and Applied Mathematics 37:3, pages 3053-3076.
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Jian-Jun Zhang, Jian-Li Zhang & Wan-Zhou Ye. (2017) An inexact alternating direction method of multipliers for the solution of linear complementarity problems arising from free boundary problems. Numerical Algorithms 78:3, pages 895-910.
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Zhong-Zhi Bai & Li-Li Zhang. (2017) Modulus-based multigrid methods for linear complementarity problems. Numerical Linear Algebra with Applications 24:6, pages e2105.
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M. Chau, A. Laouar, T. Garcia & P. Spiteri. (2016) Grid solution of problem with unilateral constraints. Numerical Algorithms 75:4, pages 879-908.
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Li-Tao Zhang, Yu-Xia Zhang, Tong-Xiang Gu, Xing-Ping Liu & Liu-Wei Zhang. (2015) New convergence of modulus-based synchronous block multisplitting multi-parameter methods for linear complementarity problems. Computational and Applied Mathematics 36:1, pages 481-492.
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Li-Tao Zhang & Tong-Xiang Gu. (2017) Global Modulus-Based Synchronous Multisplitting Multi-Parameters TOR Methods for Linear Complementarity Problems. Mathematical and Computational Applications 22:1, pages 20.
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Apostolos Hadjidimos & Michael Tzoumas. (2016) The solution of the linear complementarity problem by the matrix analogue of the accelerated overrelaxation iterative method. Numerical Algorithms 73:3, pages 665-684.
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Changfeng Ma & Na Huang. (2016) Modified modulus-based matrix splitting algorithms for a class of weakly nondifferentiable nonlinear complementarity problems. Applied Numerical Mathematics 108, pages 116-124.
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Cuiyu Liu & Chenliang Li. (2016) Synchronous and Asynchronous Multisplitting Iteration Schemes for Solving Mixed Linear Complementarity Problems with H-Matrices. Journal of Optimization Theory and Applications 171:1, pages 169-185.
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Shi-Liang Wu & Cui-Xia Li. (2016) Two-sweep modulus-based matrix splitting iteration methods for linear complementarity problems. Journal of Computational and Applied Mathematics 302, pages 327-339.
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Jun-Tao Hong & Chen-Liang Li. (2016) Modulus-based matrix splitting iteration methods for a class of implicit complementarity problems. Numerical Linear Algebra with Applications 23:4, pages 629-641.
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Na Huang & Changfeng Ma. (2016) The modulus-based matrix splitting algorithms for a class of weakly nonlinear complementarity problems. Numerical Linear Algebra with Applications 23:3, pages 558-569.
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Hua Zheng, Wen Li & Wei Qu. (2016) A non-modulus linear method for solving the linear complementarity problem. Linear Algebra and its Applications 495, pages 38-50.
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Ljiljana Cvetković, Vladimir Kostić & Ernest Šanca. (2015) A wider convergence area for the MSTMAOR iteration methods for LCP. Numerical Algorithms 71:1, pages 77-88.
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Yajun Xie & Changfeng Ma. (2015) A generalized Newton method of high-order convergence for solving the large-scale linear complementarity problem. Journal of Inequalities and Applications 2015:1.
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Na Huang & Chang-Feng Ma. (2015) Parallel multisplitting iteration methods based on M-splitting for the PageRank problem. Applied Mathematics and Computation 271, pages 337-343.
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Li-Tao Zhang, Tong-Xiang Gu & Xing-Ping Liu. (2015) Overlapping restricted additive Schwarz method with damping factor for H -matrix linear complementarity problem. Applied Mathematics and Computation 271, pages 1-10.
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Wei-wei Xu. (2015) Modified modulus-based matrix splitting iteration methods for linear complementarity problems. Numerical Linear Algebra with Applications 22:4, pages 748-760.
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Masoud Hajarian. (2014) The PMCGAOR and PMCSSOR methods for solving linear complementarity problems. Computational and Applied Mathematics 34:1, pages 251-264.
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Jian-Jun Zhang. (2014) MSSOR-based alternating direction method for symmetric positive-definite linear complementarity problems. Numerical Algorithms 68:3, pages 631-644.
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Lj. Cvetković, A. Hadjidimos & V. Kostić. (2014) On the choice of parameters in MAOR type splitting methods for the linear complementarity problem. Numerical Algorithms 67:4, pages 793-806.
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Wei-wei Xu & Hao Liu. (2014) A modified general modulus-based matrix splitting method for linear complementarity problems of H-matrices. Linear Algebra and its Applications 458, pages 626-637.
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Li-Tao Zhang, Xian-Yu Zuo, Tong-Xiang Gu & Xing-Ping Liu. (2014) Improved convergence theorems of multisplitting methods for the linear complementarity problem. Applied Mathematics and Computation 243, pages 982-987.
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Yi-Fen Ke & Chang-Feng Ma. (2014) On the convergence analysis of two-step modulus-based matrix splitting iteration method for linear complementarity problems. Applied Mathematics and Computation 243, pages 413-418.
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Ljiljana Cvetković & Vladimir Kostić. (2014) A note on the convergence of the MSMAOR method for linear complementarity problems. Numerical Linear Algebra with Applications 21:4, pages 534-539.
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Li-Tao Zhang & Jian-Lei Li. (2014) The weaker convergence of modulus-based synchronous multisplitting multi-parameters methods for linear complementarity problems. Computers & Mathematics with Applications 67:10, pages 1954-1959.
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Ning Zheng & Jun-Feng Yin. (2014) Convergence of accelerated modulus-based matrix splitting iteration methods for linear complementarity problem with an -matrix . Journal of Computational and Applied Mathematics 260, pages 281-293.
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Cuiyu Liu & Chen-liang Li. (2014) A Preconditioned Multisplitting and Schwarz Method for Linear Complementarity Problem. Journal of Applied Mathematics 2014, pages 1-6.
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Ning Zheng & Jun-Feng Yin. (2012) Accelerated modulus-based matrix splitting iteration methods for linear complementarity problem. Numerical Algorithms 64:2, pages 245-262.
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Zhong‐Zhi Bai & Li‐Li Zhang. (2012) Modulus‐based synchronous multisplitting iteration methods for linear complementarity problems. Numerical Linear Algebra with Applications 20:3, pages 425-439.
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Zhong-Zhi Bai & Li-Li Zhang. (2012) Modulus-based synchronous two-stage multisplitting iteration methods for linear complementarity problems. Numerical Algorithms 62:1, pages 59-77.
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Li-Li Zhang. (2010) Two-step modulus-based matrix splitting iteration method for linear complementarity problems. Numerical Algorithms 57:1, pages 83-99.
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Sheng-Guo Li, Hao Jiang, Li-Zhi Cheng & Xiang-Ke Liao. (2011) IGAOR and multisplitting IGAOR methods for linear complementarity problems. Journal of Computational and Applied Mathematics 235:9, pages 2904-2912.
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Zhong-Zhi Bai. (2010) Modulus-based matrix splitting iteration methods for linear complementarity problems. Numerical Linear Algebra with Applications 17:6, pages 917-933.
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Jun-Liang Dong. (2009) Shifted skew-symmetric iteration methods for nonsymmetric linear complementarity problems. Numerical Algorithms 54:3, pages 343-357.
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Qingbing Liu, Guoliang Chen & Jian Huang. (2009) On the parallel GSAOR method for block diagonally dominant matrices. Applied Mathematics and Computation 215:2, pages 707-715.
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Banxiang Duan, Xiaoping Zhu & Jiaoyu Wu. (2009) Inexact Parallel Relaxed Multisplitting Algorithm for Linear Complementarity Problem. Inexact Parallel Relaxed Multisplitting Algorithm for Linear Complementarity Problem.
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Jun-Liang Dong. (2009) Inexact multisplitting methods for linear complementarity problems. Journal of Computational and Applied Mathematics 223:2, pages 714-724.
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