Finding the spectral radius of a large sparse non-negative matrix

Abstract

A comparison of methods for finding the spectral radius of a large sparse non-negative matrix. The Arnoldi method is compared with a variation of the method of Collatz [Math Zeit, 48, 221--6, 1948], this method of Collatz being always convergent when finding the spectral radius of a non-negative matrix. The advantages and disadvantages of both methods are discussed, as well as a comparison with the methods of orthogonal iteration and simultaneous iteration. Comparisons are made using flop counts.