14 November 1989 A Jacobi-Like Algorithm For Computing The Generalized Schur Form Of A Regular Pencil
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Abstract
We develop a Jacobi-like scheme for computing the generalized Schur form of a regular pencil of matrices λB - 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. A quantitative analysis of the convergence of the method is also presented. This explains some of its peculiarities, and at the same time yields further insight in Stewart's algorithm.
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J.-P. Charlier, J.-P. Charlier, P. Van Dooren, P. Van Dooren, } "A Jacobi-Like Algorithm For Computing The Generalized Schur Form Of A Regular Pencil", Proc. SPIE 1152, Advanced Algorithms and Architectures for Signal Processing IV, (14 November 1989); doi: 10.1117/12.962271; https://doi.org/10.1117/12.962271
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