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On choosing a value of shape parameter in radial basis function collocation methods
Authors:
- Artur Krowiak,
- Jordan Podgórski
- Record ID
- CUT0a0e85dc60ff40b1abbfab0523631020
- Publication categories
- ; ;
- Author
- Pages
- [1-4]
- Other elements of collation
- tab.; wykr.; Bibliografia (na s.) - 4; Bibliografia (liczba pozycji) - 8; Oznaczenie streszczenia - Abstr.
- Book
- Simos Theodore, Theodore Simos Tsitouras Charalambos Charalambos Tsitouras (eds.): International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2018), Rhodes, Greece, 13-18 September 2018, AIP Conference Proceedings, no. 2116, 2019, [Melville], American Institute of Physics, AIP Publishing, 4 p., ISBN 978-0-7354-1854-7
- Keywords in English
- radial basis functions, collocation methods, shape parameter, conditioning of the system
- Abstract in original language
- In the paper two approaches to determine a value of shape parameter for radial basis function collocation methods are presented. This value enables to achieve very accurate results in Kansa method and radial basis function-based pseudospectral one. Both approaches are based on the estimation of the condition number of the system matrix. One of them tries to find the value of shape parameter employing a heuristic that relates the condition number to computational precision, the other one searches for the largest value of this parameter that still ensures stable computation using geometrical dependence. The presented algorithms guarantee performing computation in the stable region and are more efficient than commonly used ones. Moreover they allow to automate the computational process for these methods. In the paper the algorithms are validated by a few differential equations using multiquadrics functions. The results show that the approaches lead to high accuracy especially when non-uniform grid is applied.
- DOI
- DOI:10.1063/1.5114487 Opening in a new tab
- URL
- https://aip.scitation.org/doi/pdf/10.1063/1.5114487 Opening in a new tab
- Language
- eng (en) English
- Score (nominal)
- 20
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUT0a0e85dc60ff40b1abbfab0523631020/
- URN
urn:pkr-prod:CUT0a0e85dc60ff40b1abbfab0523631020
* presented citation count is obtained through Internet information analysis, and it is close to the number calculated by the Publish or PerishOpening in a new tab system.