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

Abstract 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.

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