• Corpus ID: 248496034

Performance of the Thresholding Greedy Algorithm with Larger Greedy Sums

@inproceedings{Chu2022PerformanceOT,
  title={Performance of the Thresholding Greedy Algorithm with Larger Greedy Sums},
  author={H{\`u}ng Việt Chu},
  year={2022}
}

• H. Chu
• Published 30 April 2022
• Computer Science, Mathematics

A BSTRACT . The goal of this note is to study the performance of the Thresholding Greedy Algorithm (TGA) when we increase the size of greedy sums by a constant factor λ ≥ 1 . We introduce the so-called ( λ , partially greedy) bases. While the case λ = 1 gives strong partially greedy bases, we show that, for each λ > 1 , there exists a (Schauder) basis that is ( λ , partially greedy) but is not strong partially greedy. Furthermore, we investigate and give examples when a basis is (1) not 1 -(almost) greedy but the TGA still gives the smallest error from an m -term approximation if we allow greedy sums to be of size ⌈ λm ⌉ , and (2) -strong partially 1 , partially greedy) for some λ > 1 . Finally, we prove various equivalences for different greedy-type bases.