In this article, we consider positive subdefinite matrices (PSBD) recently studied by J-P. Crouzeix et al. [SIAM J. Matrix Anal. Appl. 22 (2000) 66] and show that linear complementarity problems with PSBD matrices of rank greater than or equal to 2 are processable by Lemke's algorithm and that a PSBD matrix of rank greater than or equal to 2 belongs to the class of sufficient matrices introduced by R.W. Cottle et al. [Linear Algebra Appl. 114/115 (1989) 231]. We also show that if a matrix A is a sum of a merely positive subdefinite copositive plus matrix and a copositive matrix, and a feasibility condition is satisfied, then Lemke's algorithm solves LCP(q, A). This supplements the results of Jones and Evers. (C) 2001 Elsevier Science Inc. All rights reserved. [References: 11]
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