The Quasi-newton Method For The Largest Eigenvalue Of A Irreducible Nonnegative Tensor

Tensor is widely used in mathematics, physics and medical science. Irreduciblenonnegative tensor is one of the most especial tensor, and the irreducible nonnegativetensor has many points of resemblance to the irreducible nonnegative matrix. Powermethod is one of the most classic method to find the eigenvalue of a irreduciblenonnegative matrix,and the power method can be extended to find the eigenvalue of theirreducible nonnegative tensor.Newton method can be extended to find the eigenvalue ofthe irreducible nonnegative tensor too.But the convergence rateof the power method isslow.And the amount of calculation of the newton method is larger.This article introduces quasi-Newton method to find the largest eigenvalue of airreducible nonnegative tensor.At first we establish equivalent nonlinear equations,thenwe solve this quations by quasi-Newton method. In the solving process,we mustguarantee that Iterative solution is nonnegative. In this article,we will prove the globalconvergence of the quasi-Newton method under appropriate conditions,and provide thenumerical result of the quasi-Newton method comparing with the power method. Thetheoretical results and the numerical result indicate that the quasi-Newton method forfinding largest eigenvalue of a irreducible nonnegative tensor is worthy of study andpaying attention to.