On stability of Weak Greedy Algorithm in the presence of noise

TL;DR

This paper investigates the stability of weak greedy algorithms under noisy data, focusing on how small perturbations affect their convergence and robustness in approximation tasks.

Contribution

It provides theoretical results on the stability of greedy algorithms when subjected to noisy inputs, an area less explored compared to convergence properties.

Findings

Stability of greedy algorithms under noise is theoretically established.

Small data perturbations do not significantly alter the algorithm's outcome.

Results contribute to understanding robustness in greedy approximation methods.

Abstract

This paper is devoted to the theoretical study of the efficiency, namely, stability of some greedy algorithms. In the greedy approximation theory researchers are mostly interested in the following two important properties of an algorithm -- convergence and rate of convergence. In this paper we present some results on one more important property of an algorithm -- stability. Stability means that small perturbations do not result in a large change in the outcome of the algorithm. In this paper we discuss one kind of perturbations -- noisy data.