Multilevel quasi-interpolation on a sparse grid with the Gaussian

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dc.contributor.authorUsta, Fuat
dc.contributor.authorLevesley, Jeremy
dc.date.accessioned2020-04-30T23:19:24Z
dc.date.available2020-04-30T23:19:24Z
dc.date.issued2018
dc.departmentDÜ, Fen-Edebiyat Fakültesi, Matematik Bölümüen_US
dc.descriptionLevesley, Jeremy/0000-0002-3509-0152en_US
dc.descriptionWOS: 000425616500008en_US
dc.description.abstractMotivated by the recent multilevel sparse kernel-based interpolation (MuSIK) algorithm proposed in Georgoulis et al. (SIAM J. Sci. Comput. 35, 815-832, 2013), we introduce the new quasi-multilevel sparse interpolation with kernels (Q-MuSIK) via the combination technique. The Q-MuSIK scheme achieves better convergence and run time when compared with classical quasi-interpolation. Also, the Q-MuSIK algorithm is generally superior to the MuSIK methods in terms of run time in particular in high-dimensional interpolation problems, since there is no need to solve large algebraic systems. We subsequently propose a fast, low complexity, high-dimensional positive-weight quadrature formula based on Q-MuSIKSapproximation of the integrand. We present the results of numerical experimentation for both quasi-interpolation and quadrature in high dimensions.en_US
dc.identifier.doi10.1007/s11075-017-0340-yen_US
dc.identifier.endpage808en_US
dc.identifier.issn1017-1398
dc.identifier.issn1572-9265
dc.identifier.issue3en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.startpage793en_US
dc.identifier.urihttps://doi.org/10.1007/s11075-017-0340-y
dc.identifier.urihttps://hdl.handle.net/20.500.12684/3747
dc.identifier.volume77en_US
dc.identifier.wosWOS:000425616500008en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherSpringeren_US
dc.relation.ispartofNumerical Algorithmsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectQuasi-interpolationen_US
dc.subjectMultilevelen_US
dc.subjectSparse gridsen_US
dc.subjectHyperbolic crossesen_US
dc.subjectQuadratureen_US
dc.subjectHigh dimensionen_US
dc.titleMultilevel quasi-interpolation on a sparse grid with the Gaussianen_US
dc.typeArticleen_US

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