A generalized eigenvalue algorithm for tridiagonal matrix pencils based on a nonautonomous discrete integrable system

A generalized eigenvalue algorithm for a certain class of tridiagonal matrix pencils is presented. The algorithm appears as the time evolution equation of a nonautonomous discrete integrable system associated with a polynomial sequence which has some orthogonality on the support set of the zeros of the characteristic polynomial for a tridiagonal matrix pencil. The convergence of the algorithm is discussed by using the solution to the initial value problem for the corresponding discrete integrable system. (C) 2015 Elsevier B.V. All rights reserved.