In this paper, we present a modulus-based multisplitting iteration method based on multisplitting of the system matrix for a class of weakly nonlinear complementarity problem. And we prove the convergence of the method when the system matrix is an H+-matrix. Finally, we give two numerical examples.
Guangbin Wang, Fuping Tan
. Modulus-Based Multisplitting Iteration Method for a Class of Weakly Nonlinear Complementarity Problem[J]. Communications on Applied Mathematics and Computation, 2021
, 3(3)
: 419
-428
.
DOI: 10.1007/s42967-020-00074-6
1. Bai, Z.-Z.:On the convergence of the multisplitting methods for linear complementarity problem. SIAM J. Matrix Anal. Appl. 21, 67-78 (1999)
2. Bai, Z.-Z.:Modulus-based matrix splitting iteration methods for linear complementarity problems. Numer. Linear Algebra Appl. 17, 917-933 (2010)
3. Berman, A., Plemmons, R.J.:Nonnegative Matrices in the Mathematical Sciences. SIAM, Philadelphia (1994)
4. Dong, J.-L., Jiang, M.-Q.:A modified modulus method for symmetric positive-definite linear complementarity problems. Numer. Linear Algebra Appl. 16, 129-143 (2009)
5. Hadjidimos, A., Zhang, L.-L.:Comparison of three classes of algorithms for the solution of the linear complementarity problem with an H+-matrix. J. Comput. Appl. Math. 336, 175-191 (2018)
6. Huang, B.-H., Ma, C.-F.:Accelerated modulus-based matrix splitting iteration method for a class of nonlinear complementarity problems. Comp. Appl. Math. 37, 3053-3076 (2018)
7. Li, W.:A general modulus-based matrix splitting method for linear complementarity problems of H -matrices. Appl. Math. Lett. 26, 1159-1164 (2013)
8. Li, R., Yin, J.-F.:Accelerated modulus-based matrix splitting iteration methods for a restricted class of nonlinear complementarity problems. Numer. Algor. 75, 339-358 (2017)
9. Li, W., Zheng, H.:A preconditioned modulus-based iteration method for solving linear complementarity problems of H-matrices. Linear Multilinear Algebra 64, 1390-1403 (2016)
10. Luo, M.-J., Wang, Y.-Y., Liu, H.-L.:Convergence results of a matrix splitting algorithm for solving weakly nonlinear complementarity problems. J. Inequal. Appl. 203, 1-9 (2016)
11. Van Bokhoven, W.M.G.:Piecewise-Linear Modelling and Analysis. Proefschrift, Eindhoven (1981)
12. Varga, R.S.:Matrix Iterative Analysis. Springer, Berlin (2000)
13. Wu, Y.-J., Yan, G.-L., Yang, A.-L.:Modulus-based synchronous multisplitting iteration methods for a restricted class of nonlinear complementarity problems. Numer. Math. Theory Methods Appl. 12, 709-726 (2019)
14. Xia, Z.-C., Li, C.-L.:Modulus-based matrix splitting iteration methods for a class of nonlinear complementarity problem. Appl. Math. Comput. 271, 34-42 (2015)
15. Xu, W.-W., Liu, H.:A modified general modulus-based matrix splitting method for linear comple mentarity problems of H-matrices. Linear Algebra Appl. 458, 626-637 (2014)
16. Xu, H.-R., Chen, R.-L., Xie, S.-L., Wu, L.:Modulus-based multisplitting iteration methods for a class of nonlinear complementarity problems. E. Asian J. Appl. Math. 8, 519-530 (2018)
17. Zheng, N., Yin, J.-F.:Convergence of accelerated modulus-based matrix splitting iteration methods for linear complementarity problem with an H+-matrix. J. Comput. Appl. Math. 260, 281-293 (2014)
