On the entropy numbers and the Kolmogorov widths

TL;DR

This paper establishes new direct estimates linking Kolmogorov widths and entropy numbers using Lipschitz widths, with applications to m-term approximation, advancing understanding of approximation theory.

Contribution

It introduces direct estimates between widths and entropy numbers via Lipschitz widths, providing new tools for approximation analysis.

Findings

Derived direct estimates between Kolmogorov widths and entropy numbers.

Applied these estimates to m-term approximation problems.

Enhanced theoretical understanding of approximation measures.

Abstract

Direct estimates between linear or nonlinear Kolmogorov widths and entropy numbers are presented. These estimates are derived using the recently introduced Lipschitz widths. Applications for m-term approximation are obtained.