A Method of Calculating the Spectral Radius of a Nonnegative Matrix and its Applications

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. Keywords and Phrases: Leontief model, Productiviy, Market equilibrium, Spectral radius, M-matrices, Geometric programming