Close-to-optimal bounds for loop approximation
type: Item
instance of: scholarly article
title: Close-to-optimal bounds for loop approximation
zbMATH Open document ID: 1206.41012
author: Peter Oswald
author: Tatiana Shingel
published in: Journal of Approximation Theory
publication date: 2010-11-18T00:00:00Z
review text: The authors continue the investigations of [J. Approx. Theory 161, No. 1, 174--186 (2009; Zbl 1177.22013)] and prove the following result: Let \(N\geq 2\), \(\alpha>1\) and \(\varepsilon>0\). For any \(U(t)\in \text{Lip}_{\alpha}(\mathbb T\rightarrow \text{SU}(N))\), there exists a sequence of \(\text{SU}(N)\)-valued polynomial loops \(U_{n}(t)\) of degree \(\leq n\) such that \[ \|U-U_{n}\|_C\leq C_{\alpha,\varepsilon,N,U}(n+1)^{-(\alpha-\varepsilon)}, \quad n\geq 0. \]
reviewed by: Stamatis Koumandos
Mathematics Subject Classification ID: 41A29
Mathematics Subject Classification ID: 41A46
Mathematics Subject Classification ID: 22E67
zbMATH DE Number: 5817247
zbMATH Keywords: nonlinearly constrained approximation
zbMATH Keywords: loop groups
zbMATH Keywords: Jackson-type estimates
zbMATH Keywords: paraunitary FIR filters
zbMATH Keywords: splitting methods
MaRDI profile type: Publication
full work available at URL: j.jat.2010.04.006
OpenAlex ID: W1999287372
cites work: Q4273944
cites work: Hermite interpolation in loop groups and conjugate quadrature filter approximation
cites work: Splitting methods
cites work: Splitting methods for SU\((N)\) loop approximation
cites work: Q3754832
cites work: Decomposition formulas of exponential operators and Lie exponentials with some applications to quantum mechanics and statistical physics
cites work: Q3138779
DOI: 10.1016/J.JAT.2010.04.006
description: scientific article; zbMATH DE number 5817247