The distance of a subspace of \(R^ m\) from its axes and n-widths of octahedra
type: Item
instance of: scholarly article
title: The distance of a subspace of \(R^ m\) from its axes and n-widths of octahedra
zbMATH Open document ID: 0556.41016
DOI: 10.1016/0021-9045(84)90042-X
author: Avraham A. Melkman
published in: Journal of Approximation Theory
publication date: 1984-01-01T00:00:00Z
review text: Necessary and sufficient conditions for the existence of an n-dimensional subspace of \(R^ m\) with given \(\ell^ m_ p\) distances from the principal axes are established, and used to derive exact results and estimates for the n-widths of diagonal operators from \(\ell^ m_ 1\) to \(\ell^ m_ p\). In particular, evidence is presented to support the conjecture that the asymptotic value of \(d_ n(I;\ell^ m_ 1,\ell^ m_ p)\) is \(m^{1/p}\sqrt{1-\alpha}/\sqrt{n}\) where \(\alpha =\lim n/m\).
Mathematics Subject Classification ID: 41A46
zbMATH DE Number: 3886507
zbMATH Keywords: n-widths of diagonal operators
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3886507