Super Greedy Type Algorithms

TL;DR

This paper introduces super greedy algorithms that select multiple dictionary elements per step, showing they achieve similar error bounds as standard greedy algorithms for incoherent dictionaries while being computationally simpler.

Contribution

It demonstrates that super greedy algorithms match the error bounds of standard greedy algorithms for incoherent dictionaries and are computationally more efficient.

Findings

Super greedy algorithms achieve comparable error bounds to standard greedy algorithms.

Super greedy algorithms are computationally simpler than their standard counterparts.

The phenomenon holds for incoherent dictionaries.

Abstract

We study greedy-type algorithms such that at a greedy step we pick several dictionary elements contrary to a single dictionary element in standard greedy-type algorithms. We call such greedy algorithms {\it super greedy algorithms}. The idea of picking several elements at a greedy step of the algorithm is not new. Recently, we observed the following new phenomenon. For incoherent dictionaries these new type of algorithms (super greedy algorithms) provide the same (in the sense of order) upper bound for the error as their analogues from the standard greedy algorithms. The super greedy algorithms are computationally simpler than their analogues from the standard greedy algorithms. We continue to study this phenomenon.