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arXiv · 2602.01421

Convergence Analysis of Greedy Algorithms with Adaptive Relaxation in Hilbert Spaces

Pablo M. Berná·Andrea García
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Abstract

The Power-Relaxed Greedy Algorithm (PRGA) was introduced as a generalization of the so called Relaxed Greedy Algorithm, introduced by DeVore and Temlyakov, by replacing the relaxation parameter $1/m$ with $1/m^\alpha$, with the aim of improving convergence rates. While the case $\alpha\le 1$ is well understood, the behavior of the algorithm for $\alpha>1$ remained an open problem. In this work, we answer this question and, moreover, we introduce a relaxed greedy algorithm with an optimal step size chosen by exact line search at each iteration.

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BibTeXRIS

Pablo M. Berná, Andrea García. 2026-02-01. Convergence Analysis of Greedy Algorithms with Adaptive Relaxation in Hilbert Spaces. https://arxiv.org/abs/2602.01421

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