A new algorithm for computing largest real part eigenvalue of matrices: Collatz & Perron-Frobernius' approach

This paper describes a new method and algorithm for the numerical solution of eigenvalues with the largest real part of positive matrices. The method is based on a numerical implementation of Collatz's eigenvalue inclusion theorem for non-negative irreducible matrices. Eigenvalues are analyzed for the studies of the stability of linear systems. Finally, a numerical discussion is given to derive the required number of mathematical operations of the new algorithm. Comparisons between the new algorithm and several well known ones, such as Power, and QR methods, are discussed.