In the core of the study of the model that describes an LSS we find the quadratic eigenproblem (QE) Kz = lambda^2 Mz + lambda Cz of size n. The most popular technique to date, for the QE, first transforms it to a linear eigenproblem (LE) Ax = lambda Bx, of size 2n and then solves the LE, with obvious disadvantages. Our main objective is to develop algorithms for the QE that will operate on size n data instead. We intend to use techniques, in the spirit of the QZ algorithm, such as deflation, implicit shifts and double steps.

Revised: 1994.10.13