Equilibrium eigenvector

Crude estimates of the equilibrium eigenvector may be obtained by successive squaring, but better estimates are usually needed. A fairly recent article [26] utilizes an approximation to the matrix resolvent --- itself both an eigenvector matrix and a positive matrix for a suitable range of its parameter --- to characterize polyhedra confining the equilibrium eigenvector. Namely, if L is a positive matrix of lower bounds to the matrix A, and is an upper bound to , the rows (or columns) of the resolvent

can be used to form the cages.

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Harold V. McIntosh
E-mail:mcintosh@servidor.unam.mx