A divide-and-conquer method for the tridiagonal generalized eigenvalue problem

Abstract

We introduce a divide-and-conquer method for the generalized eigenvalue problem Ax = λBx, where A and B are real symmetric tridiagonal matrices and B is positive-definite. It is a generalization of Cuppen's method for the standard eigenvalue problem, B = I, which is based on rank-one modifications. Our method is an alternative to a method developed by Borges and Gragg using restrictions and extensions.