Vector greedy algorithms

Authors:
Adam Lutoborski;Vladimir N. Temlyakov
Affiliations:
Department of Mathematics, Syracuse University, Syracuse, NY;Department of Mathematics, University of South Carolina, Columbia, SC
Venue:
Journal of Complexity
Year:
2003

Citing 3
Cited 5

Nonlinear approximation in finite-dimensional spaces

Journal of Complexity
Greedy algorithms and M-term approximation with regard to redundant dictionaries

Journal of Approximation Theory
Greedy algorithms and applications

Greedy algorithms and applications

Simultaneous greedy approximation in Banach spaces

Journal of Complexity
Algorithms for simultaneous sparse approximation: part I: Greedy pursuit

Signal Processing - Sparse approximations in signal and image processing
Simultaneous greedy approximation in Banach spaces

Journal of Complexity
Colour image coding with matching pursuit in the spatio-frequency domain

ICIAP'11 Proceedings of the 16th international conference on Image analysis and processing: Part I
Column subset selection via sparse approximation of SVD

Theoretical Computer Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

Our objective is to study nonlinear approximation with regard to redundant systems. Redundancy on the one hand offers much promise for greater efficiency in terms of approximation rate, but on the other hand gives rise to highly nontrivial theoretical and practical problems. Greedy-type approximations proved to be convenient and efficient ways of constructing m-term approximants. We introduce and study vector greedy algorithms that are designed with aim of constructing mth greedy approximants simultaneously for a given finite number of elements. We prove convergence theorems and obtain some estimates for the rate of convergence of vector greedy algorithms when elements come from certain classes.