The LZ Algorithm to Solve the Generalized Eigenvalue Problem.

摘要

The LZ algorithm is a method for solving the generalized eigenvalue problem where one is given two square matrices A and B and asked to find the scalar lambda and the vector x such that Ax =lambda Bx. In the paper,the author analyzes certain aspects of the LZ algorithm and discusses various alternative approaches to different parts of the algorithm. In particular,the author performs a backward error analysis of the algorithm and discusses various shift strategies and criteria for convergence. Several direct methods are described which may be substituted for the first phase of the LZ method where A is reduced to upper Hessenberg form and B to upper triangular form. (Author)