Sample complexity of worst-case \(H^\infty\)-identification
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.
scientific article; zbMATH DE number 984387