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## "Push-the-Error" algorithm for nonlinear n-term approximation

A 2004 Preprint by W. Dahmen and P. Petrushev

• 2004:07
• This paper is concerned with further developing and refining the analysis of a recent algorithmic paradigm for nonlinear approximation termed "Push-the-error" scheme. It is especially designed to deal with $L _ \infty$ 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 funtional $N(\varepsilon)$ counting the number of terms needed to achieve accuracy $\varepsilon$. This allows one to show that the improved scheme captures all rates of best n-term approximation.

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