Abstract
In this paper, we consider some relaxed synchronous and asynchronous multisplitting iteration schemes for solving the mixed linear complementarity problems, with the matrix A being H-matrix. We establish some convergence theorems for the methods. Numerical results show that the new methods are efficient and suitable to parallel computing.
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Frommer, A., Schwandt, H.: A unified representation and theory of algebraic additive Schwarz and multisplitting methods. SIAM J. Martrix Anal. Appl. 18, 893–912 (1997)
Frommer, A., Schwandt, H., Szyld, D.B.: Asynchronous weighted additive Schwarz methods. Electron. Trans. Numer. Anal. 5, 48–61 (1997)
Mangasarian, O.L., De Leone, R.: Parallel successive overrelaxation methods for symmetric linear complementarity problems and linear programs. J. Optim. Theory. Appl. 54, 437–446 (1987)
Machida, N., Fukushima, M., Ibaraki, T.: A multisplitting method for symmetric linear complementarity problems. J. Comput. Appl. Math. 62, 217–227 (1995)
Bai, Z.Z.: On the convergence of the multisplitting methods for the linear complementarity problem. SIAM J. Matrix Anal. Appl. 21, 67–78 (1999)
Bai, Z.Z.: On the monotone convergence of matrix multisplitting relaxation methods for the linear complementarity problem. IMA J. Numer. Anal. 18, 509–518 (1998)
Bai, Z.Z., Evans, D.J.: Matrix multisplitting relaxation methods for linear complementarity problems. Int. J. Comput. Math. 63, 309–326 (1997)
Bai, Z.Z., Evans, D.J.: Asynchronous multisplitting relaxation methods for linear complementarity problems. Int. J. Comput. Math. 70, 519–538 (1999)
Bai, Z.Z.: A class of generalized multisplitting relaxation methods for linear complementarity problems. Appl. Math. J. Chin. Univ. 13B, 188–198 (1998)
Bai, Z.Z., Evans, D.J.: Matrix multisplitting methods with applications to linear complementarity problems: parallel synchronous and chaotic methods. Reseaux et systemes repartis: Calculateurs Paralleles 13, 125–154 (2001)
Bai, Z.Z., Evans, D.J.: Matrix multisplitting methods with applications to linear complementarity problems: parallel asynchronous methods. Int. J. Comput. Math. 79, 205–232 (2002)
De Leone, R., Mangasarian, O.L.: Asynchronous parallel successive overrelaxation for symmetric linear complementarity problem. Math. Program. 42, 347–361 (1988)
Bai, Z.Z.: Modulus-based matrix splitting iteration methods for linear complementarity problems. Numer. Linear Algebra Appl. 17, 917–933 (2010)
Bai, Z.Z., Zhang, L.L.: Modulus-based synchronous multisplitting iteration methods for linear complementarity problems. Numer. Linear Algebra Appl. 20, 425–439 (2013)
Zhang, L.L.: Two-step modulus-based synchronous multisplitting iteration methods for linear complementarity problems. J. Comput. Math. 33, 100–112 (2015)
Bai, Z.Z., Sun, J.C., Wang, D.R.: A unified framework for the construction of various matrix multisplitting iterative methods for large sparse system of linear equations. Comput. Math. Appl. 32, 51–76 (1996)
Li, D.H., Zeng, J.P.: Iterative solution for two-sided obstacle problems. J. Numer. Methods Comput. Appl. (Chin.) 3, 194–199 (1994)
Acknowledgments
The authors are most grateful to the referees for providing very useful comments and suggestions, which greatly improved the original manuscript of this paper. This work was supported by Natural Science Foundation of China (11161014) and Guangxi Natural Science Foundation (2015GXNSFAA139014, 2014GXNSFAA118004).
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Communicated by Francis Tin-Loi.
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Liu, C., Li, C. Synchronous and Asynchronous Multisplitting Iteration Schemes for Solving Mixed Linear Complementarity Problems with H-Matrices. J Optim Theory Appl 171, 169–185 (2016). https://doi.org/10.1007/s10957-016-0944-8
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DOI: https://doi.org/10.1007/s10957-016-0944-8