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Franz, Tino ; Wendland, Holger:
Multilevel quasi-interpolation.
In: IMA Journal of Numerical Analysis.
Bd. 43
(2023)
.
- S. 2934-2964.
ISSN 1464-3642
DOI: https://doi.org/10.1093/imanum/drac059
Abstract
Quasi-interpolation methods are well-established tools in multivariate approximation. They are efficient as they do not require, in contrast to interpolation, the solution of a linear system. Quasi-interpolations are often first studied on infinite grids. Here, it is usually required that the quasi-interpolation operator reproduces polynomials of a certain degree exactly. This degree corresponds to the approximation order of the quasi-interpolation process. Unfortunately, if a radial, compactly supported kernel is employed for building the quasi-interpolation operator, it is well known that polynomial reproduction is impossible in two or more dimensions. As such operators are numerically appealing and are frequently used in particle methods, we will, in this paper, look at such quasi-interpolation operators that do not reproduce polynomials and show that they lead, when employed in a multilevel scheme, to an efficient and converging approximation method.
Weitere Angaben
| Publikationsform: | Artikel in einer Zeitschrift |
|---|---|
| Begutachteter Beitrag: | Ja |
| Institutionen der Universität: | Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik III (Angewandte und Numerische Analysis) > Lehrstuhl Mathematik III (Angewandte und Numerische Analysis) - Univ.-Prof. Dr. Holger Wendland |
| Titel an der UBT entstanden: | Ja |
| Themengebiete aus DDC: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Eingestellt am: | 06 Mär 2024 08:34 |
| Letzte Änderung: | 06 Mär 2024 08:34 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/88800 |