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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.01421 |
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| _version_ | 1866918318205566976 |
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| author | Berná, Pablo M. García, Andrea |
| author_facet | Berná, Pablo M. García, Andrea |
| contents | 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 $1/m^α$, with the aim of improving convergence rates. While the case $α\le 1$ is well understood, the behavior of the algorithm for $α>1$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01421 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Convergence Analysis of Greedy Algorithms with Adaptive Relaxation in Hilbert Spaces Berná, Pablo M. García, Andrea Functional Analysis 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 $1/m^α$, with the aim of improving convergence rates. While the case $α\le 1$ is well understood, the behavior of the algorithm for $α>1$ 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. |
| title | Convergence Analysis of Greedy Algorithms with Adaptive Relaxation in Hilbert Spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2602.01421 |