Browsing by Author "Sivakumar, K.C."

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Complementarity properties of singular M-matrices
(2016) Jeyaraman, I.; Sivakumar, K.C.
For a matrix A whose off-diagonal entries are nonpositive, its nonnegative invertibility (namely, that A is an invertible M-matrix) is equivalent to A being a P-matrix, which is necessary and sufficient for the unique solvability of the linear complementarity problem defined by A. This, in turn, is equivalent to the statement that A is strictly semimonotone. In this paper, an analogue of this result is proved for singular symmetric Z-matrices. This is achieved by replacing the inverse of A by the group generalized inverse and by introducing the matrix classes of strictly range semimonotonicity and range column sufficiency. A recently proposed idea of P#-matrices plays a pivotal role. Some interconnections between these matrix classes are also obtained. 2016 Elsevier Inc.
Complementarity properties of singular M-matrices
(Elsevier Inc. usjcs@elsevier.com, 2016) Jeyaraman, I.; Sivakumar, K.C.
For a matrix A whose off-diagonal entries are nonpositive, its nonnegative invertibility (namely, that A is an invertible M-matrix) is equivalent to A being a P-matrix, which is necessary and sufficient for the unique solvability of the linear complementarity problem defined by A. This, in turn, is equivalent to the statement that A is strictly semimonotone. In this paper, an analogue of this result is proved for singular symmetric Z-matrices. This is achieved by replacing the inverse of A by the group generalized inverse and by introducing the matrix classes of strictly range semimonotonicity and range column sufficiency. A recently proposed idea of P#-matrices plays a pivotal role. Some interconnections between these matrix classes are also obtained. © 2016 Elsevier Inc.
Extensions of p-property, r0-property and semidefinite linear complementarity problems
(2017) Jeyaraman, I.; Bisht, K.; Sivakumar, K.C.
In this manuscript, we present some new results for the semidefinite linear complementarity problem in the context of three notions for linear transformations, viz., pseudo w-P property, pseudo Jordan w-P property, and pseudo SSM property. Interconnections with the P#-property (proposed recently in the literature) are presented. We also study the R#-property of a linear transformation, extending the rather well known notion of an R0-matrix. In particular, results are presented for the Lyapunov, Stein, and the multiplicative transformations.
Extensions of p-property, r0-property and semidefinite linear complementarity problems
(Faculty of Organizational Sciences, Belgrade, 2017) Jeyaraman, I.; Bisht, K.; Sivakumar, K.C.
In this manuscript, we present some new results for the semidefinite linear complementarity problem in the context of three notions for linear transformations, viz., pseudo w-P property, pseudo Jordan w-P property, and pseudo SSM property. Interconnections with the P#-property (proposed recently in the literature) are presented. We also study the R#-property of a linear transformation, extending the rather well known notion of an R0-matrix. In particular, results are presented for the Lyapunov, Stein, and the multiplicative transformations.