{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T10:29:24Z","timestamp":1778495364224,"version":"3.51.4"},"reference-count":13,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,5,16]],"date-time":"2021-05-16T00:00:00Z","timestamp":1621123200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,5,16]],"date-time":"2021-05-16T00:00:00Z","timestamp":1621123200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100004281","name":"Narodowe Centrum Nauki","doi-asserted-by":"publisher","award":["2017\/25\/B\/ST1\/00945"],"award-info":[{"award-number":["2017\/25\/B\/ST1\/00945"]}],"id":[{"id":"10.13039\/501100004281","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2022,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We present an asymptotic analysis of adaptive methods for <jats:italic>L<\/jats:italic><jats:sup><jats:italic>p<\/jats:italic><\/jats:sup> approximation of functions <jats:italic>f<\/jats:italic> \u2208 <jats:italic>C<\/jats:italic><jats:sup><jats:italic>r<\/jats:italic><\/jats:sup>([<jats:italic>a<\/jats:italic>, <jats:italic>b<\/jats:italic>]), where <jats:inline-formula><jats:alternatives><jats:tex-math>$1\\le p\\le +\\infty $<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mn>1<\/mml:mn>\n                  <mml:mo>\u2264<\/mml:mo>\n                  <mml:mi>p<\/mml:mi>\n                  <mml:mo>\u2264<\/mml:mo>\n                  <mml:mo>+<\/mml:mo>\n                  <mml:mi>\u221e<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. The methods rely on piecewise polynomial interpolation of degree <jats:italic>r<\/jats:italic> \u2212\u20091 with adaptive strategy of selecting <jats:italic>m<\/jats:italic> subintervals. The optimal speed of convergence is in this case of order <jats:italic>m<\/jats:italic><jats:sup>\u2212<jats:italic>r<\/jats:italic><\/jats:sup> and it is already achieved by the uniform (nonadaptive) subdivision of the initial interval; however, the asymptotic constant crucially depends on the chosen strategy. We derive asymptotically best adaptive strategies and show their applicability to automatic <jats:italic>L<\/jats:italic><jats:sup><jats:italic>p<\/jats:italic><\/jats:sup> approximation with a given accuracy <jats:italic>\u03b5<\/jats:italic>.<\/jats:p>","DOI":"10.1007\/s11075-021-01114-9","type":"journal-article","created":{"date-parts":[[2021,5,16]],"date-time":"2021-05-16T04:02:30Z","timestamp":1621137750000},"page":"277-302","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Automatic approximation using asymptotically optimal adaptive interpolation"],"prefix":"10.1007","volume":"89","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8704-0790","authenticated-orcid":false,"given":"Leszek","family":"Plaskota","sequence":"first","affiliation":[]},{"given":"Pawe\u0142","family":"Samoraj","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,5,16]]},"reference":[{"key":"1114_CR1","volume-title":"Methods of Numerical Integration, 2nd edn","author":"P Davis","year":"1984","unstructured":"Davis, P., Rabinowitz, P.: Methods of Numerical Integration, 2nd edn. 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