{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T05:12:39Z","timestamp":1770268359855,"version":"3.49.0"},"reference-count":30,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11671213"],"award-info":[{"award-number":["11671213"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11271199"],"award-info":[{"award-number":["11271199"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2020,7]]},"abstract":"<jats:p> We study the Kolmogorov and the linear approximation numbers of the Besov classes [Formula: see text] with mixed smoothness in the norm of [Formula: see text] in the randomized setting. We first establish two discretization theorems. Then based on them, we determine the exact asymptotic orders of the Kolmogorov and the linear approximation numbers for certain values of the parameters [Formula: see text]. Our results show that the linear randomized methods lead to considerably better rates than those of the deterministic ones for [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s021969132050023x","type":"journal-article","created":{"date-parts":[[2020,2,13]],"date-time":"2020-02-13T07:57:02Z","timestamp":1581580622000},"page":"2050023","source":"Crossref","is-referenced-by-count":3,"title":["Randomized approximation numbers on Besov classes with mixed smoothness"],"prefix":"10.1142","volume":"18","author":[{"given":"Liqin","family":"Duan","sequence":"first","affiliation":[{"name":"Mathematics and Science College, Shanghai Normal University, Shanghai 200234, 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. 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