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Erschienen in:
13.06.2016
On estimating the separation of two periodic matrix sequences
Erschienen in: BIT Numerical Mathematics | Ausgabe 1/2017
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Abstract
The sensitivity of solutions to the periodic Sylvester equation \(A_kX_k-X_{k\oplus 1}B_k\)
\(=C_k, k=0, 1, \ldots , K-1,\) is primarily dependent on the quantity
introduced by Granat and Kågström (SIAM J Matrix Anal Appl 28:285–300, 2006) in connection with the resolution to periodic invariant subspaces of a product of matrices. In this paper, we give some lower and upper bounds of
based on periodic Schur decompositions, which are generalizations of those of the separation between two matrices. Numerical examples are presented to illustrate the theoretical results.
introduced by Granat and Kågström (SIAM J Matrix Anal Appl 28:285–300, 2006) in connection with the resolution to periodic invariant subspaces of a product of matrices. In this paper, we give some lower and upper bounds of
based on periodic Schur decompositions, which are generalizations of those of the separation between two matrices. Numerical examples are presented to illustrate the theoretical results.