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.