240 IGPM240.pdf        March 2004
TITLE "Push-the-Error'' Algorithm for Nonlinear N-Term Approximation
AUTHORS Wolfgang Dahmen, Pencho Petrushev
ABSTRACT This paper is concerned with further developing and rening the analysis of a recent algorithmic paradigm for nonlinear approximation termed \Push-the-Error" scheme. It is especially designed to deal with L1 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(") counting the number of terms needed to achieve accuracy ". This allows one to show that the improved scheme captures all rates of best n-term approximation.
KEYWORDS uniform norm approximation, multilevel expansions, wavelet bases, best n-term approximation
DOI 10.1007/s00365-005-0607-8
PUBLICATION Constructive approximation
23(3), 261-304 (2006)