Periodic Schur decomposition: algorithms and applications

Adam W. Bojanczyk; Gene H. Golub; Paul Van Dooren

doi:10.1117/12.130915

30 November 1992 Periodic Schur decomposition: algorithms and applications

Adam W. Bojanczyk, Gene H. Golub, Paul Van Dooren

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Proceedings Volume 1770, Advanced Signal Processing Algorithms, Architectures, and Implementations III; (1992) https://doi.org/10.1117/12.130915
Event: San Diego '92, 1992, San Diego, CA, United States

Abstract

In this paper we derive a unitary eigendecomposition for a sequence of matrices which we call the periodic Schur decomposition. We prove its existence and discuss its application to the solution of periodic difference equations arising in control. We show how the classical QR algorithm can be extended to provide a stable algorithm for computing this generalized decomposition. We apply the decomposition also to cyclic matrices and two point boundary value problems. Key words. Numerical algorithms, linear algebra, periodic systems, K-cyclic matrices, two-point boundary value problems

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Adam W. Bojanczyk, Gene H. Golub, and Paul Van Dooren "Periodic Schur decomposition: algorithms and applications", Proc. SPIE 1770, Advanced Signal Processing Algorithms, Architectures, and Implementations III, (30 November 1992); https://doi.org/10.1117/12.130915

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