Abstract
This paper is concerned with further developing and refining the analysis of a recent algorithmic paradigm for nonlinear approximation, termed the "Push-the-Error" scheme. It is especially designed to deal with L∞-approximation in a multilevel framework. The original version is extended considerably to cover all commonly used multiresolution frameworks. The main conceptually new result is the proof of the quasi-semi-additivity of the functional N(ε) counting the number of terms needed to achieve accuracy ε. This allows one to show that the improved scheme captures all rates of best n-term approximation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Dahmen, W., Petrushev, P. "Push-the-Error" Algorithm for Nonlinear n-Term Approximation. Constr Approx 23, 261–304 (2006). https://doi.org/10.1007/s00365-005-0607-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00365-005-0607-8