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Article

Almost Optimality of the Orthogonal Super Greedy Algorithm for μ-Coherent Dictionaries †

by
Chunfang Shao
1,*,
Jincai Chang
1,
Peixin Ye
2,
Wenhui Zhang
2 and
Shuo Xing
2
1
College of Science, North China University of Science and Technology, Tangshan 063210, China
2
School of Mathematics and LPMC, Nankai University, Tianjin 300071, China
*
Author to whom correspondence should be addressed.
†
This work was supported by National Natural Science Foundation of China under Grant 11671213.
Axioms 2022, 11(5), 186; https://doi.org/10.3390/axioms11050186
Submission received: 29 January 2022 / Revised: 7 April 2022 / Accepted: 12 April 2022 / Published: 20 April 2022
(This article belongs to the Special Issue Numerical Computation, Approximation of Functions and Applied Mathematics)
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Abstract

We study the approximation capability of the orthogonal super greedy algorithm (OSGA) with respect to μ-coherent dictionaries in Hilbert spaces. We establish the Lebesgue-type inequalities for OSGA, which show that the OSGA provides an almost optimal approximation on the first [1/(18μs)] steps. Moreover, we improve the asymptotic constant in the Lebesgue-type inequality of OGA obtained by Livshitz E D.
Keywords: orthogonal super greedy algorighm; coherence; best n-term approximation; Lebesgue-type inequality orthogonal super greedy algorighm; coherence; best n-term approximation; Lebesgue-type inequality

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MDPI and ACS Style

Shao, C.; Chang, J.; Ye, P.; Zhang, W.; Xing, S. Almost Optimality of the Orthogonal Super Greedy Algorithm for μ-Coherent Dictionaries. Axioms 2022, 11, 186. https://doi.org/10.3390/axioms11050186

AMA Style

Shao C, Chang J, Ye P, Zhang W, Xing S. Almost Optimality of the Orthogonal Super Greedy Algorithm for μ-Coherent Dictionaries. Axioms. 2022; 11(5):186. https://doi.org/10.3390/axioms11050186

Chicago/Turabian Style

Shao, Chunfang, Jincai Chang, Peixin Ye, Wenhui Zhang, and Shuo Xing. 2022. "Almost Optimality of the Orthogonal Super Greedy Algorithm for μ-Coherent Dictionaries" Axioms 11, no. 5: 186. https://doi.org/10.3390/axioms11050186

APA Style

Shao, C., Chang, J., Ye, P., Zhang, W., & Xing, S. (2022). Almost Optimality of the Orthogonal Super Greedy Algorithm for μ-Coherent Dictionaries. Axioms, 11(5), 186. https://doi.org/10.3390/axioms11050186

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