An Alternating Sequence Iteration’s Method for Computing Largest Real Part Eigenvalue of Essentially Positive Matrices: Collatz and Perron-Frobernius’ Approach

Tedja Santanoe Oepomo

Abstract

This paper describes a new numerical method for the numerical solution of eigenvalues with the largest real part of essentially positive matrices. Finally, a numerical discussion is given to derive the required number of mathematical operations of the new method. Comparisons between the new method and several well know ones, such as Power and QR methods, were discussed. The process consists of computing lower and upper bounds which are monotonically approximating the eigenvalue.