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A method of calculating the spectral radius of a nonnegative matrix and its applications

Author

Listed:
  • Marat Ibragimov

    (Tashkent State Economic University, Ul. Uzbekistanskaya, 49, 700063 Tashkent, UZBEKISTAN)

Abstract

We present a method of calculating the maximal eigenvalue of an indecomposable nonnegative matrix, which is based on ideas of geometric programming. In addition to that, we obtain estimates for elements of an indecomposable nonnegative matrix by its spectral radius. The results make it possible to obtain new necessary conditions for the productivity of the matrix of coefficients in the Leontief input-output model and have the immediate relation to the analysis of M- matrices. Another interesting application of the developed method is given by conditions of stability of the dynamic system of market equilibrium.

Suggested Citation

  • Marat Ibragimov, 2001. "A method of calculating the spectral radius of a nonnegative matrix and its applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 17(2), pages 467-480.
    • Handle: RePEc:spr:joecth:v:17:y:2001:i:2:p:467-480
    Note: Received: January 20, 1999; revised version: November 9, 1999
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    Cited by:

    1. Christis Katsouris, 2021. "Optimal Portfolio Choice and Stock Centrality for Tail Risk Events," Papers 2112.12031, arXiv.org.

    More about this item

    Keywords

    Leontief model; Productiviy; Market equilibrium; Spectral radius; M-matrices; Geometric programming.;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C67 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Input-Output Models

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