{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:11:44Z","timestamp":1753884704795,"version":"3.41.2"},"reference-count":18,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","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":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2022,9]]},"abstract":"<jats:p> In this paper, we obtain the unified error estimate for some weak biorthogonal greedy algorithms with respect to dictionaries in Banach spaces by using some kind of K-functional. From this estimate, we derive the sufficient conditions for the convergence and the convergence rates on sparse classes induced by the K-functional. The results on convergence and the convergence rates are sharp. <\/jats:p>","DOI":"10.1142\/s0219691322500102","type":"journal-article","created":{"date-parts":[[2022,4,13]],"date-time":"2022-04-13T15:39:10Z","timestamp":1649864350000},"source":"Crossref","is-referenced-by-count":4,"title":["Unified error estimate for weak biorthogonal Greedy algorithms"],"prefix":"10.1142","volume":"20","author":[{"given":"Bing","family":"Jiang","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peixin","family":"Ye","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenhui","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2022,4,12]]},"reference":[{"key":"S0219691322500102BIB001","doi-asserted-by":"publisher","DOI":"10.1214\/009053607000000631"},{"key":"S0219691322500102BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2019.108286"},{"key":"S0219691322500102BIB003","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492900002816"},{"key":"S0219691322500102BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/BF02124742"},{"key":"S0219691322500102BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2020.108885"},{"key":"S0219691322500102BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/BF02678464"},{"key":"S0219691322500102BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2015.12.011"},{"issue":"2","key":"S0219691322500102BIB008","doi-asserted-by":"crossref","first-page":"186","DOI":"10.4213\/mzm2581","volume":"78","author":"Galatenko V. V.","year":"2005","journal-title":"Mat. Zametki"},{"key":"S0219691322500102BIB009","doi-asserted-by":"publisher","DOI":"10.1142\/S0219691321500016"},{"key":"S0219691322500102BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-35347-9"},{"key":"S0219691322500102BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/s10092-016-0183-2"},{"key":"S0219691322500102BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2015.10.008"},{"key":"S0219691322500102BIB013","doi-asserted-by":"publisher","DOI":"10.3934\/ipi.2015.9.231"},{"key":"S0219691322500102BIB014","doi-asserted-by":"publisher","DOI":"10.1023\/A:1016657209416"},{"issue":"12","key":"S0219691322500102BIB015","volume":"2","author":"Temlyakov V. N.","year":"2014","journal-title":"Forum. Math. Sigma"},{"key":"S0219691322500102BIB016","doi-asserted-by":"publisher","DOI":"10.1007\/s10114-005-0913-x"},{"key":"S0219691322500102BIB017","doi-asserted-by":"publisher","DOI":"10.1142\/S0219691317500291"},{"key":"S0219691322500102BIB018","doi-asserted-by":"publisher","DOI":"10.1142\/S1793536912500264"}],"container-title":["International Journal of Wavelets, Multiresolution and Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219691322500102","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,24]],"date-time":"2022-08-24T08:19:06Z","timestamp":1661329146000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0219691322500102"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,12]]},"references-count":18,"journal-issue":{"issue":"05","published-print":{"date-parts":[[2022,9]]}},"alternative-id":["10.1142\/S0219691322500102"],"URL":"https:\/\/doi.org\/10.1142\/s0219691322500102","relation":{},"ISSN":["0219-6913","1793-690X"],"issn-type":[{"type":"print","value":"0219-6913"},{"type":"electronic","value":"1793-690X"}],"subject":[],"published":{"date-parts":[[2022,4,12]]},"article-number":"2250010"}}