{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T03:04:24Z","timestamp":1760151864964,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,4,20]],"date-time":"2022-04-20T00:00:00Z","timestamp":1650412800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11671213"],"award-info":[{"award-number":["11671213"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We study the approximation capability of the orthogonal super greedy algorithm (OSGA) with respect to \u03bc-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\/(18\u03bcs)] steps. Moreover, we improve the asymptotic constant in the Lebesgue-type inequality of OGA obtained by Livshitz E D.<\/jats:p>","DOI":"10.3390\/axioms11050186","type":"journal-article","created":{"date-parts":[[2022,4,21]],"date-time":"2022-04-21T01:55:51Z","timestamp":1650506151000},"page":"186","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Almost Optimality of the Orthogonal Super Greedy Algorithm for \u03bc-Coherent Dictionaries"],"prefix":"10.3390","volume":"11","author":[{"given":"Chunfang","family":"Shao","sequence":"first","affiliation":[{"name":"College of Science, North China University of Science and Technology, Tangshan 063210, China"}]},{"given":"Jincai","family":"Chang","sequence":"additional","affiliation":[{"name":"College of Science, North China University of Science and Technology, Tangshan 063210, China"}]},{"given":"Peixin","family":"Ye","sequence":"additional","affiliation":[{"name":"School of Mathematics and LPMC, Nankai University, Tianjin 300071, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6202-8311","authenticated-orcid":false,"given":"Wenhui","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and LPMC, Nankai University, Tianjin 300071, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5585-6215","authenticated-orcid":false,"given":"Shuo","family":"Xing","sequence":"additional","affiliation":[{"name":"School of Mathematics and LPMC, Nankai University, Tianjin 300071, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1017\/S0962492900002816","article-title":"Nonlinear approximation","volume":"7","author":"DeVore","year":"1998","journal-title":"Acta Numer."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1214\/009053607000000631","article-title":"Approximation and learning by greedy algorithms","volume":"36","author":"Barron","year":"2008","journal-title":"Ann. 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Eng."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/5\/186\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:57:13Z","timestamp":1760137033000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/5\/186"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,20]]},"references-count":20,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["axioms11050186"],"URL":"https:\/\/doi.org\/10.3390\/axioms11050186","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2022,4,20]]}}}