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Monte Carlo integration of $C^{r}$ functions with adaptive variance reduction: an asymptotic analysis

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cris.lastimport.scopus2024-02-12T19:57:40Z
dc.abstract.enThe theme of the present paper is numerical integration of Cr functions using randomized methods. We consider variance reduction methods that consist in two steps. First the initial interval is partitioned into subintervals and the integrand is approximated by a piecewise polynomial interpolant that is based on the obtained partition. Then a randomized approximation is applied on the difference of the integrand and its interpolant. The final approximation of the integral is the sum of both. The optimal convergence rate is already achieved by uniform (nonadaptive) partition plus the crude Monte Carlo; however, special adaptive techniques can substantially lower the asymptotic factor depending on the integrand. The improvement can be huge in comparison to the nonadaptive method, especially for functions with rapidly varying rth derivatives, which has serious implications for practical computations. In addition, the proposed adaptive methods are easily implementable and can be well used for automatic integration.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorPlaskota, Leszek
dc.contributor.authorStępień, Łukasz
dc.contributor.authorPrzybyłowicz, Paweł
dc.date.accessioned2024-01-25T12:54:13Z
dc.date.available2024-01-25T12:54:13Z
dc.date.copyright2023-05-22
dc.date.issued2023
dc.description.accesstimeAT_PUBLICATION
dc.description.financePublikacja bezkosztowa
dc.description.number2
dc.description.versionFINAL_PUBLISHED
dc.description.volume63
dc.identifier.doi10.1007/S10543-023-00972-0
dc.identifier.issn0006-3835
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/112931
dc.identifier.weblinkhttps://link.springer.com/article/10.1007/s10543-023-00972-0
dc.languageeng
dc.pbn.affiliationmathemathics
dc.relation.ispartofBIT Numerical Mathematics
dc.relation.pages32: 1-24
dc.rightsCC-BY
dc.sciencecloudnosend
dc.subject.enMonte Carlo
dc.subject.enAdaption
dc.subject.enVariance reduction
dc.subject.enAsymptotic constants
dc.titleMonte Carlo integration of $C^{r}$ functions with adaptive variance reduction: an asymptotic analysis
dc.typeJournalArticle
dspace.entity.typePublication