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An Algebraic Approach to Hankel Norm Approximation Problems

  • The polynomial approach introduced in Fuhrmann [1991] is extended to cover the crucial area of AAK theory, namely the characterization of zero location of the Schmidt vectors of the Hankel operators. This is done using the duality theory developed in that paper but with a twist. First we get the standard, lower bound, estimates on the number of unstable zeroes of the minimal degree Schmidt vectors of the Hankel operator. In the case of the Schmidt vector corresponding to the smallest singular the lower bound is in fact achieved. This leads to a solution of a Bezout equation. We use this Bezout equation to introduce another Hankel operator which have singular values that are the inverse of the singular values of the original Hankel operator.

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Author:Paul A. Fuhrmann
URN (permanent link):urn:nbn:de:hbz:386-kluedo-6873
Serie (Series number):Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (81)
Document Type:Preprint
Language of publication:English
Year of Completion:1992
Year of Publication:1992
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2000/10/17
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011