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High-dimensional approximation with kernel-based multilevel methods on sparse grids

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00007423
URN to cite this document: urn:nbn:de:bvb:703-epub-7423-7

Title data

Kempf, Rüdiger ; Wendland, Holger:
High-dimensional approximation with kernel-based multilevel methods on sparse grids.
In: Numerische Mathematik. Vol. 154 (2023) Issue 3 . - pp. 485-519.
ISSN 0029-599X
DOI der Verlagsversion: https://doi.org/10.1007/s00211-023-01363-x

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Project information

Project financing: Deutsche Forschungsgemeinschaft

Abstract

Moderately high-dimensional approximation problems can successfully be solved by combining univariate approximation processes using an intelligent combination technique. While this has so far predominantly been done with either polynomials or splines, we suggest to employ a multilevel kernel-based approximation scheme. In contrast to those schemes built upon polynomials and splines, this new method is capable of combining arbitrary low-dimensional domains instead of just intervals and arbitrarily distributed points in these low-dimensional domains. We introduce the method and analyse its convergence in the so-called isotropic and anisotropic cases.

Further data

Item Type: Article in a journal
Subject classification: 65D12 65D15 46E22 41A63
DDC Subjects: 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
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-7423-7
Date Deposited: 19 Jan 2024 09:41
Last Modified: 19 Jan 2024 09:42
URI: https://epub.uni-bayreuth.de/id/eprint/7423
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