Convergence Rate for the Method of Finding the Largest Eigen value of Nonnegative Weakly Irreducible Polynomials

Eigenvalue problem can be found in many fields such as aquatic conservation, ship structure and marine energy system. In 2014, an algorithm for finding the largest eigenvalue of nonnegative polynomials was introduced by Ibrahim. The method has been proven to be convergent but its rate of convergence has not been discussed in literature. In this paper we will show that the rate of convergence for the algorithm is linear under weak irreducibility condition. Index Terms - Convergence rate, Iterative method, Eigenvalue, Polynomial.