A Jacobi-like algorithm for computing the generalized Schur form of a regular pencil

摘要

We develop a Jacobi-like scheme for computing the generalized Schur form ofa regular pencil of matrices σB − A. The method starts with a preliminary triangularization of the matrix B and iteratively reduces A to triangular form, while maintaining B triangular. The scheme heavily relies on the technique of Stewart for computing the Schur form of an arbitrary matrix A. Just as Stewart's algorithm, this one can efficiently be implemented in parallel on a square array of processors. This explains some of its peculiarities, and at the same time yields further insight in Stewart's algorithm.