A note on Murthy's conjecture

• Autorzy: Li J.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we consider a conjecture made by Murthy to the effect that a [..] matrix is positive semidefinite (PSD) and show that the conjecture is true for n x n matrices of rank 1 or 3 x 3 matrices that are not in Q. We also consider the class of P1-matrices which is a subclass of QQ and obtain the following: for [...] PSD for n < 3 and A isn't PSD for n > 3.

Słowa kluczowe

EN

linear complementarity problem; PSD-matrices; Murthy's conjecture

PL

liniowy problem dopełniający; macierze; PSD-macierze; hipoteza Murthy'sa

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2007
• Tom: Vol. 40, nr 4
• Strony: 963--969
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Li J.

• Faculty of Applied Mathematics, Guangdong University of Technology, Guangzhou 510090, P. R. China,

Bibliografia

• [1] R. W. Cottle, J. S. Pang, and R. E. Stone, The Linear Complementarity Problem[M], New York, Academic Press, 1992.
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• [3] G. S. R. Murthy and T. Parthasarathy, Fully copositivc matrices[J], Math. Programming 82 (1998), 401-411.
• [4] G. S. R. Murthy, T. Parthasarathy and B. Sriparna, Some recent results on the linear complementarity problem[J], SIAM J. Matrix Anal. Appl. 19 (1998), 898-905.
• [5] G. S. R. Murthy, T. Parthasarathy and B. Sriparna, On the solution sets of linear complementarity problems[J], SIAM J. Matrix Anal. Appl. 21 (2000), 1229-1235.
• [6] S. R. Mohan, S. K. Neogy and A. K. Das, On the classes of fully copositive and fully seminotone matrices [J], Linear Algebra Appl. 323 (2001), 87-97.
• [7] G. S. R. Murthy, S. R. Neogy and F. Thuijsman, A note on P1 and Lipschitzian matrices[J], SIAM J. Matrix Anal. Appl. 21 (1999), 636-641.
• [8] R. A. Danao, A note on E'-matrices[J], Linear Algebra Appl. 259 (1997), 299-305.
• [9] R. A. Danao, On a class of semimonotone Qo-matrices in the linear complementarity problem[J], Operations Research Letters 13 (1993), 121-125.