Eigenvalue Computation of Totally Nonnegative Upper Hessenberg Matrices Based on a Variant of the Discrete Hungry Toda Equation

摘要

The integrable discrete hungry Toda (dhToda) equation has already been applied to design an eigenvalue algorithm which computes eigenvalues of totally nonnegative (TN) matrices with lower Hessenberg form. In this paper, an eigenvalue algorithm for computing eigenvalues of TN matrices with upper Hessenberg form is derived based on a variant of the dhToda equation.