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Numerical Aspects of the Tensor Product Multilevel Method for High-Dimensional, Kernel-Based Reconstruction on Sparse Grids

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00008948
URN to cite this document: urn:nbn:de:bvb:703-epub-8948-3

Title data

Büttner, Markus ; Kempf, Rüdiger ; Wendland, Holger:
Numerical Aspects of the Tensor Product Multilevel Method for High-Dimensional, Kernel-Based Reconstruction on Sparse Grids.
In: Journal of Scientific Computing. Vol. 106 (2026) . - 8.
ISSN 1573-7691
DOI der Verlagsversion: https://doi.org/10.1007/s10915-025-03144-0

Format:	PDF
Name:	s10915-025-03144-0.pdf
Version:	Published Version
Available under License	Creative Commons BY 4.0: Attribution

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Project information

Project title:	Project's official title Project's id Kernbasierte Multilevelverfahren für hochdimensionale Approximationsprobleme auf dünnen Gittern - Herleitung, Analyse und Anwendung in der Uncertainty Quantification 452806809 Open Access Publizieren No information
Project financing:	Deutsche Forschungsgemeinschaft

Abstract

This paper investigates the approximation of functions with finite smoothness defined on domains with a Cartesian product structure. The recently proposed tensor product multilevel method (TPML) combines Smolyak’s sparse grid method with a kernel-based residual correction technique. The contributions of this paper are twofold. First, we present two improvements on the TPML that reduce the computational cost of point evaluations compared to a naive implementation. Second, we provide numerical examples that demonstrate the effectiveness and innovation of the TPML.

Further data

Item Type:	Article in a journal
DDC Subjects:	000 Computer Science, information, general works > 004 Computer science 500 Science > 500 Natural sciences 500 Science > 510 Mathematics
Institutions of the University:	Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics III (Applied and Numerical Analysis) > Chair Mathematics III (Applied and Numerical Analysis) - Univ.-Prof. Dr. Holger Wendland Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Scientific Computing Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics III (Applied and Numerical Analysis)
Language:	English
Originates at UBT:	Yes
URN:	urn:nbn:de:bvb:703-epub-8948-3
Date Deposited:	03 Mar 2026 08:13
Last Modified:	06 Mar 2026 12:43
URI:	https://epub.uni-bayreuth.de/id/eprint/8948

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