Abstract
In this paper, a new direct algorithm for solving linear complementarity problem with Z-matrix is proposed. The algorithm exhibits either a solution or its nonexistence after at most, steps (where n is the dimension of the problem) and the computational complexity is at most1/3n3 + O(n2)
Similar content being viewed by others
References
Cottle, R. W.. Giannessi, F. and Lions,J. L., (eds.), Variational Inequalities and Complementarity-Problems. Theorey and Applications, John Wiley &. Sons, 1980.
Cottle, R. W., Pang, J. S. and Stone, R. E., The Linear Complementarity Problem, AP, New, York, 1992.
Cryer, C. W., The efficient solution of linear complementarity problems for tridiagonal Minkowski matrices, ACM Trans. Math. Soflzvare, 9(1983), 199–214.
Murty, K. G., Linear Complementarity, Linear and Nonlinear Programming, Heldermann, Berlin. 1988.
Zeng, J. P. and Zhou.S. Z. Two-side obstacle’problem and its equivalent linear complementarity problem, Chinese Science Bulletin, 39(1994), 1057–1062.
Zhang, L. and Hu,X. Y. On the direct method for linear complementarity problem, Math. Numer. Sinica, 1(1994), 59–64.
Zhou, S. Z., On the convergence of an algorithm of Uzawa’s type for saddlepoint problems, Chinese Science Bulletin, 30(1985), 1531–1534.
Zhou, S. Z., A direct method for the linear complementarity problem, J. Compta. Math., 2(1990), 178–182.
Author information
Authors and Affiliations
Additional information
The research is supported by NNSF of China.
Rights and permissions
About this article
Cite this article
Donghui, L., Jinping, Z. & Zhongzhi, Z. Gaussian pivoting method for solving linear complementarity problem. Appl. Math. Chin. Univ. 12, 419–426 (1997). https://doi.org/10.1007/s11766-997-0044-5
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s11766-997-0044-5