Sample complexity of worst-case \(H^\infty\)-identification
type: Item
instance of: scholarly article
title: Sample complexity of worst-case \(H^\infty\)-identification
zbMATH Open document ID: 0913.93014
DOI: 10.1016/0167-6911(96)80520-2
author: O. Diekmann
published in: Systems \& Control Letters
publication date: 1997-02-27T00:00:00Z
review text: The paper deals with the sample complexity of worst case \(H^\infty\)-identification. It is shown that the above complexity is of order \(n^2\). The result is based on the proof that the minimal length of a fractional \(H^\infty\)-cover for \(\mathbb{C}^n\) viewed as the linear space of complex-valued sequences of length \(n\) is of order \(n^2\). A fractional \(H^\infty\)-cover for \(C^n\) is represented by a unit vector \(u\) in \(l^\infty\) if for some \(0< \alpha<1\), \(\| u*h\|_\infty\geq \alpha\| \widetilde{h} \|_{H^\infty}\) for all \(h\in \mathbb{C}^n\), where \(\widetilde{h}(z)= \sum_{j=0}^{n-1} h_jz^j\) is the \(z\)-transform of \(h\). Similar results are given for real-valued sequences.
Mathematics Subject Classification ID: 93B30
Mathematics Subject Classification ID: 93B36
zbMATH DE Number: 984387
zbMATH Keywords: Sample complexity
zbMATH Keywords: Fractional cover
zbMATH Keywords: \(\alpha\)-cover
zbMATH Keywords: \(H^{\infty}\)-cover
zbMATH Keywords: Real \(\alpha\)-cover
zbMATH Keywords: worst case \(H^\infty\)-identification
reviewed by: Liviu Goraş
MaRDI profile type: Publication
full work available at URL: 0167-6911(96)80520-2
OpenAlex ID: W1996859466
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description: scientific article; zbMATH DE number 984387