On testing nonnegativity of principal minors of $${\mathbf {Z}}$$ Z -matrices using simplex method

Dipti Dubey () and S. K. Neogy ()
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Dipti Dubey: Shiv Nadar University
S. K. Neogy: Indian Statistical Institute

Annals of Operations Research, 2022, vol. 315, issue 2, No 15, 985-992

Abstract: Abstract A real square matrix is a $${\mathbf {Z}}$$ Z -matrix if it’s off diagonal elements are nonpositive. A $${\mathbf {Z}}$$ Z -matrix with nonnegative principal minors is called an $${\mathbf {M}}$$ M -matrix. The problem of testing whether a given matrix is an $${\mathbf {M}}$$ M -matrix or not is an important research problem in matrix theory as $${\mathbf {M}}$$ M -matrices arise naturally in a wide range of applications including finite difference methods for partial differential equations, input-output models in economics, linear complementarity problems in operations research, and Markov processes in probability and statistics. In this paper, we present a polynomial-time algorithm for testing whether a $${\mathbf {Z}}$$ Z -matrix is an $${\mathbf {M}}$$ M -matrix based on modified simplex method.

Keywords: $${\mathbf {Z}}$$ Z -matrix; $${\mathbf {P}}_{0}$$ P 0 -matrix; $${\mathbf {M}}$$ M -matrix; Linear Complementarity Problem; Simplex Method; 90C33; 90C05 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10479-021-04095-z

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