Diagonal transformation methods for computing the maximal eigenvalue and eigenvector of a nonnegative irreducible matrix

Computation of Bounds for the Positive Eigenvector of a Nonnegative Irreducible Matrix by Monotone Iteration

A method for the computation of iterative bounds for the positive eigenvector of a nonnegative irreducible matrix is presented. It is based on the P-boundedness of the corresponding fixed point operator. Admissible initial bounds can be obtained by conditional preiteration.

Maximal nonnegative perturbation of a nonnegative matrix

is known to be stable if and only if ρ(A) < 1. Models of real world dynamical phenomena often involve positive quantities. A dynamical system (1) is called positive if any trajectory of the system starting in the positive orthant R+ remains in R+. In this case, the matrix A has only real positive entries. In many cases, it may be useful to consider systems with a known “nominal” part A and a un...

On Eigenvalue and Eigenvector Estimates for Nonnegative Definite Operators

In this article we further develop a perturbation approach to the Rayleigh– Ritz approximations from our earlier work. We both sharpen the estimates and extend the applicability of the theory to nonnegative definite operators . The perturbation argument enables us to solve two problems in one go: We determine which part of the spectrum of the operator is being approximated by the Ritz values an...

AN ALGORITHM FOR COMPUTING THE PERRON ROOT OF A NONNEGATIVE IRREDUCIBLE MATRIX by PRAKASH CHANCHANA

CHANCHAN, PRAKASH. An Algorithm for Computing the Perron Root of a Nonnegative Irreducible Matrix. (Under the direction of Carl D. Meyer.) We present a new algorithm for computing the Perron root of a nonnegative irreducible matrix. The algorithm is formulated by combining a reciprocal of the well known Collatz’s formula with a special inverse iteration algorithm discussed in [10, Linear Algebr...

A Complex Neural Network Algorithm for Computing the Largest Real Part Eigenvalue and the corresponding Eigenvector of a Real Matrix