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

Author

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  • Dipti Dubey

    (Shiv Nadar University)

  • S. K. Neogy

    (Indian Statistical Institute)

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.

Suggested Citation

  • Dipti Dubey & S. K. Neogy, 2022. "On testing nonnegativity of principal minors of $${\mathbf {Z}}$$ Z -matrices using simplex method," Annals of Operations Research, Springer, vol. 315(2), pages 985-992, August.
    • Handle: RePEc:spr:annopr:v:315:y:2022:i:2:d:10.1007_s10479-021-04095-z
    DOI: 10.1007/s10479-021-04095-z
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    References listed on IDEAS

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    1. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
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