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

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Author Info
Marat Ibragimov () (Tashkent State Economic University, Ul. Uzbekistanskaya, 49, 700063 Tashkent, UZBEKISTAN)

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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.

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Publisher Info
Article provided by Springer in its journal Economic Theory.

Volume (Year): 17 (2001)
Issue (Month): 2 ()
Pages: 467-480
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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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Related research
Keywords: Leontief model; Productiviy; Market equilibrium; Spectral radius; M-matrices; Geometric programming.;

Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium
C67 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Input-Output Models

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This page was last updated on 2009-11-25.

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