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

Elsner L, Fasse A, Langmann E. A divide-and-conquer method for the tridiagonal generalized eigenvalue problem. Journal of Computational and Applied Mathematics. 1997;86(1):141-148.We introduce a divide-and-conquer method for the generalized eigenvalue problem Ax = lambda Bx, 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