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Periodic Schur decomposition: algorithms and applications

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.