Finite test sets and $P$-matrices
HTML articles powered by AMS MathViewer
- by Michael M. Kostreva PDF
- Proc. Amer. Math. Soc. 84 (1982), 104-105 Request permission
Abstract:
The class of matrices with all principal minors positive, known as $P$-matrices, has been characterized by Murty and Tamir using a finite set of test vectors for the linear complementarity problem. This paper refines their characterizations by deriving a set of test vectors which has lower cardinality and vectors which are more easily tested.References
- Hans Samelson, R. M. Thrall, and Oscar Wesler, A partition theorem for Euclidean $n$-space, Proc. Amer. Math. Soc. 9 (1958), 805–807. MR 97025, DOI 10.1090/S0002-9939-1958-0097025-0
- Katta G. Murty, On the number of solutions to the complementarity problem and spanning properties of complementary cones, Linear Algebra Appl. 5 (1972), 65–108. MR 291183, DOI 10.1016/0024-3795(72)90019-5
- Katta G. Murty, On a characterization of $P$-matrices, SIAM J. Appl. Math. 20 (1971), 378–384. MR 292868, DOI 10.1137/0120041
- Arie Tamir, On a characterization of $P$-matrices, Math. Programming 4 (1973), 110–112. MR 323798, DOI 10.1007/BF01584650
- C. E. Lemke, Bimatrix equilibrium points and mathematical programming, Management Sci. 11 (1964/65), 681–689. MR 189823, DOI 10.1287/mnsc.11.7.681
- C. B. Garcia, Some classes of matrices in linear complementarity theory, Math. Programming 5 (1973), 299–310. MR 337312, DOI 10.1007/BF01580135
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 104-105
- MSC: Primary 90C33; Secondary 15A06, 65K05
- DOI: https://doi.org/10.1090/S0002-9939-1982-0633288-1
- MathSciNet review: 633288