On testing nonnegativity of principal minors of Z-matrices using simplex method

A real square matrix is a Z -matrix if it’s off diagonal elements are nonpositive. A Z -matrix with nonnegative principal minors is called an M -matrix. The problem of testing whether a given matrix is an M -matrix or not is an important research problem in matrix theory as M -matrices arise natural...

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Bibliographic Details
Published in:Annals of operations research 2022-08, Vol.315 (2), p.985-992
Main Authors: Dubey, Dipti, Neogy, S. K.
Format: Article
Language:English
Subjects:
Algorithms
Business and Management
Combinatorics
Economic models
Finite difference method
Markov processes
Matrix theory
Operations research
Operations Research/Decision Theory
Partial differential equations
Polynomials
S.I.: Business Analytics and Operations Research
Simplex method
Theory of Computation
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Summary:A real square matrix is a Z -matrix if it’s off diagonal elements are nonpositive. A Z -matrix with nonnegative principal minors is called an M -matrix. The problem of testing whether a given matrix is an M -matrix or not is an important research problem in matrix theory as 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 Z -matrix is an M -matrix based on modified simplex method.
ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-021-04095-z