ISSN:
1435-568X
Keywords:
Hankel norm
;
Rational approximation
;
Order of approximation
;
Wiener class
Source:
Springer Online Journal Archives 1860-2000
Topics:
Electrical Engineering, Measurement and Control Technology
,
Mathematics
,
Technology
Notes:
Abstract The problem of approximating Hankel operators of infinite rank by finite-rank Hankel operators is considered. For efficiency, truncated infinite Hankel matrices Γn of Γ are utilized. In this paper for any compact Hankel operator Γ of the Wiener class, we derive the rate of l2-convergence of the Schmidt pairs of Γn to the corresponding Schmidt pairs of Γ. For a certain subclass of Hankel operators of the Wiener class, we also obtain the rate of l1-convergence. In addition, an upper bound for the rate of uniform convergence of the rational symbols of best rank-k Hankel approximants of Γn to the corresponding rational symbol of the best rank-k Hankel approximant to Γ asn → ∞ is derived.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01211976
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