An always convergent method for finding the spectral radius of an irreducible non-negative matrix

Abstract

An always convergent method is used to calculate the spectral radius of an irreducible non-negative matrix. The method is an adaptation of a method of Collatz (1942), and has similarities to both the power method and the inverse power method. For large matrices it is faster than the eig routine in Matlab. Special attention is paid to the step-by-step improvement of the bounds and the subsequent convergence of this method.