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Numerical Algorithms
Published in: Numerical Algorithms 4/2021

29-05-2020 | Original Paper

A two-step modulus-based matrix splitting iteration method for horizontal linear complementarity problems

Authors: Hua Zheng, Seakweng Vong

Published in: Numerical Algorithms | Issue 4/2021

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Abstract

In this paper, for solving horizontal linear complementarity problems, a two-step modulus-based matrix splitting iteration method is established. The convergence analysis of the proposed method is presented, including the case of accelerated overrelaxation splitting. Numerical examples are reported to show the efficiency of the proposed method.
previous article Numerical treatment of the generalized Love integral equation

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Literature
1.
Alanelli, M., Hadjidimos, A.: A new iterative criterion for H-matrices. SIAM J. Matrix Anal. Appl. 29, 160–176 (2006)MathSciNetCrossRef
2.
Bai, Z. -Z.: On the convergence of the multisplitting methods for the linear complementarity problem. SIAM J. Matrix Anal. Appl. 21, 67–78 (1999)MathSciNetCrossRef
3.
Bai, Z. -Z.: Modulus-based matrix splitting iteration methods for linear complementarity problems. Numer. Linear Algebra Appl. 17, 917–933 (2010)MathSciNetCrossRef
4.
Bai, Z. -Z., Zhang, L. -L.: Modulus-based synchronous multisplitting iteration methods for linear complementarity problems. Numer. Linear Algebra Appl. 20, 425–439 (2013)MathSciNetCrossRef
5.
Bai, Z. -Z., Zhang, L. -L.: Modulus-based synchronous two-stage multisplitting iteration methods for linear complementarity problems. Numer. Algorithm. 62, 59–77 (2013)MathSciNetCrossRef
6.
Berman, A., Plemmons, R. J.: Nonnegative Matrix in the Mathematical Sciences. SIAM Publisher, Philadelphia (1994)CrossRef
7.
Bru, R., Giménez, I., Hadjidimos, A.: Is a ∈ cn×n a general H-matrix?. Linear Algebra Appl. 436, 364–380 (2012)MathSciNetCrossRef
8.
Cottle, R. W., Dantzig, G. B.: A generalization of the linear complementarity problem. J. Comb. Theory 8, 79–90 (1970)MathSciNetCrossRef
9.
Cottle, R. W., Pang, J. S., Stone, R. E.: The Linear Complementarity Problem. Academic, San Diego (1992)MATH
10.
Fang, X. -M., Zhu, Z. -w.: The modulus-based matrix double splitting iteration method for linear complementarity problems. Comput. Math. Appl. 78(11), 3633–3643 (2019)MathSciNetCrossRef
11.
Frommer, A., Mayer, G.: Convergence of relaxed parallel multisplitting methods. Linear Algebra Appl. 119, 141–152 (1989)MathSciNetCrossRef
12.
13.
Fujisawa, T., Kuh, E. S., Ohtsuki, T.: A sparse matrix method for analysis of piecewise-linear resistive networks. IEEE Trans. Circ. Theory 19, 571–584 (1972)MathSciNetCrossRef
14.
Gao, X., Wang, J.: Analysis and application of a one-layer neural network for solving horizontal linear complementarity problems. Int. J. Comput. Int. Sys. 7(4), 724–732 (2014)CrossRef
15.
Giacopini, M., Fowell, M., Dini, D., Strozzi, A.: A mass-conserving complementarity formulation to study lubricant films in the presence of cavitation. J. Tribol. 132, 041702 (2010)CrossRef
16.
Hu, J. -G.: Estimates of \(||{b^{-1}c}||_{\infty }\) and their applications. Math. Numer. Sin. 4, 272–282 (1982)
17.
Huang, N., Ma, C. -F.: The modulus-based matrix splitting algorithms for a class of weakly nonlinear complementarity problems. Numer. Linear Algebra Appl. 23, 558–569 (2016)MathSciNetCrossRef
18.
Li, W.: A general modulus-based matrix splitting method for linear complementarity problems of H-matrices. Appl. Math. Lett. 26, 1159–1164 (2013)MathSciNetCrossRef
19.
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)MathSciNetCrossRef
20.
Liu, S. -M., Zheng, H., Li, W.: A general accelerated modulus-based matrix splitting iteration method for solving linear complementarity problems. Calcolo 53, 189–199 (2016)MathSciNetCrossRef
21.
Mezzadri, F., Galligani, E.: An inexact Newton method for solving complementarity problems in hydrodynamic lubrication. Calcolo 55, 1 (2018)MathSciNetCrossRef
22.
Mezzadri, F., Galligani, E.: Splitting methods for a class of horizontal linear complementarity problems. J. Optim. Theory Appl. 180(2), 500–517 (2019)MathSciNetCrossRef
23.
Mezzadri, F., Galligani, E.: Modulus-based matrix splitting methods for horizontal linear complementarity problems. Numer. Algorithm. 83, 201–219 (2020)MathSciNetCrossRef
24.
25.
26.
Sun, M.: Monotonicity of Mangasarian’s iterative algorithm for generalized linear complementarity problems. J. Math. Anal. Appl. 144, 474–485 (1989)MathSciNetCrossRef
27.
28.
Sznajder, R., Gowda, M. S.: Generalizations of p0- and P-properties; extended vertical and horizontal linear complementarity problems. Linear Algebra Appl. 223(/224), 695–715 (1995)MathSciNetCrossRef
29.
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)MathSciNetMATH
30.
Zhang, L. -L.: Two-step modulus based matrix splitting iteration for linear complementarity problems. Numer. Algorithm. 57, 83–99 (2011)MathSciNetCrossRef
31.
Zhang, L. -L., Ren, Z. -R.: Improved convergence theorems of modulus-based matrix splitting iteration methods for linear complementarity problems. Appl. Math. Lett. 26, 638–642 (2013)MathSciNetCrossRef
32.
Zheng, H.: Improved convergence theorems of modulus-based matrix splitting iteration method for nonlinear complementarity problems of H-matrices. Calcolo 54, 1481–1490 (2017)MathSciNetCrossRef
33.
Zheng, H., Li, W.: The modulus-based nonsmooth Newton’s method for solving linear complementarity problems. J. Comput. Appl. Math. 288, 116–126 (2015)MathSciNetCrossRef
34.
Zheng, H., Li, W., Vong, S.: A relaxation modulus-based matrix splitting iteration method for solving linear complementarity problems. Numer. Algorithm. 74, 137–152 (2017)MathSciNetCrossRef
35.
Zheng, H., Li, W., Vong, S.: An iteration method for nonlinear complementarity problems. J. Comput. Appl. Math. 372, 112681 (2020)MathSciNetCrossRef
36.
Zheng, H., Liu, L.: A two-step modulus-based matrix splitting iteration method for solving nonlinear complementarity problems of h+-matrices. Comput. Appl. Math. 37(4), 5410–5423 (2018)MathSciNetCrossRef
37.
Zheng, H., Vong, S.: The modulus-based nonsmooth Newton’s method for solving a class of nonlinear complementarity problems of P-matrices. Calcolo. 55, 37 (2018)MathSciNetCrossRef
38.
Zheng, H., Vong, S., Liu, L.: A direct precondition modulus-based matrix splitting iteration method for solving linear complementarity problems. Appl. Math. Comput. 353, 396–405 (2019)MathSciNetMATH
39.
Zheng, H., Vong, S.: Improved convergence theorems of the two-step modulus-based matrix splitting and synchronous multisplitting iteration methods for solving linear complementarity problems. Linear Multilinear Algebra. 67 (9), 1773–1784 (2019)MathSciNetCrossRef
40.
Zheng, H., Vong, S.: A modified modulus-based matrix splitting iteration method for solving implicit complementarity problems. Numer. Algorithm. 82(2), 573–592 (2019)MathSciNetCrossRef
41.
Zheng, H., Vong, S.: On convergence of the modulus-based matrix splitting iteartion method for horizontal linear complementarity problem of h+-matrices. Appl. Math. Comput. 369, 124890 (2020)MathSciNetMATH
42.
Zheng, N., Yin, J. -F.: Accelerated modulus-based matrix splitting iteration methods for linear complementarity problems. Numer. Algorithm. 64, 245–262 (2013)MathSciNetCrossRef
Metadata
Title
A two-step modulus-based matrix splitting iteration method for horizontal linear complementarity problems
Authors
Hua Zheng
Seakweng Vong
Publication date
29-05-2020
Publisher
Springer US
Published in
Numerical Algorithms / Issue 4/2021
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-020-00954-1

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