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Automatic approximation using asymptotically optimal adaptive interpolation

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cris.lastimport.scopus2024-02-12T20:44:28Z
dc.abstract.enWe present an asymptotic analysis of adaptive methods for Lp approximation of functions f ∈ Cr([a, b]), where 1≤p≤+∞. The methods rely on piecewise polynomial interpolation of degree r − 1 with adaptive strategy of selecting m subintervals. The optimal speed of convergence is in this case of order m−r 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 Lp approximation with a given accuracy ε.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorSamoraj, Paweł
dc.contributor.authorPlaskota, Leszek
dc.date.accessioned2024-01-24T16:59:21Z
dc.date.available2024-01-24T16:59:21Z
dc.date.copyright2021-05-16
dc.date.issued2022
dc.description.accesstimeAT_PUBLICATION
dc.description.financePublikacja bezkosztowa
dc.description.number1
dc.description.versionFINAL_PUBLISHED
dc.description.volume89
dc.identifier.doi10.1007/S11075-021-01114-9
dc.identifier.issn1017-1398
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/101354
dc.identifier.weblinkhttps://link.springer.com/content/pdf/10.1007/s11075-021-01114-9.pdf
dc.languageeng
dc.pbn.affiliationmathemathics
dc.relation.ispartofNumerical Algorithms
dc.relation.pages277-302
dc.rightsCC-BY
dc.sciencecloudnosend
dc.subject.enNumerical (automatic) approximation
dc.subject.enAdaptive algorithms
dc.subject.enAsymptotic constants
dc.titleAutomatic approximation using asymptotically optimal adaptive interpolation
dc.typeJournalArticle
dspace.entity.typePublication