Computing Periodic Deflating Subspaces Associated with a Specified Set of Eigenvalues
نویسنده
چکیده
We present a direct method for reordering eigenvalues in the generalized periodic real Schur form of a regular K-cyclic matrix pair sequence (Ak, Ek). Following and generalizing existing approaches, reordering consists of consecutively computing the solution to an associated Sylvester-like equation and constructingK pairs of orthogonal matrices. These pairs define an orthogonal K-cyclic equivalence transformation that swaps adjacent diagonal blocks in the Schur form. An error analysis of this swapping procedure is presented, which extends existing results for reordering eigenvalues in the generalized real Schur form of a regular pair (A,E). Our direct reordering method is used to compute periodic deflating subspace pairs corresponding to a specified set of eigenvalues. This computational task arises in various applications related to discretetime periodic descriptor systems. Computational experiments confirm the stability and reliability of the presented eigenvalue reordering method. AMS subject classification (2000): 65F15, 15A18, 93B60.
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