Skala, V. and Karim, S.A.A. and Cervenka, M. (2020) Finding points of importance for radial basis function approximation of large scattered data. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 12142 . pp. 239-250. ISSN 03029743
Full text not available from this repository.Abstract
Interpolation and approximation methods are used in many fields such as in engineering as well as other disciplines for various scientific discoveries. If the data domain is formed by scattered data, approximation methods may become very complicated as well as time-consuming. Usually, the given data is tessellated by some method, not necessarily the Delaunay triangulation, to produce triangular or tetrahedral meshes. After that approximation methods can be used to produce the surface. However, it is difficult to ensure the continuity and smoothness of the final interpolant along with all adjacent triangles. In this contribution, a meshless approach is proposed by using radial basis functions (RBFs). It is applicable to explicit functions of two variables and it is suitable for all types of scattered data in general. The key point for the RBF approximation is finding the important points that give a good approximation with high precision to the scattered data. Since the compactly supported RBFs (CSRBF) has limited influence in numerical computation, large data sets can be processed efficiently as well as very fast via some efficient algorithm. The main advantage of the RBF is, that it leads to a solution of a system of linear equations (SLE) Ax = b. Thus any efficient method solves the systems of linear equations that can be used. In this study is we propose a new method of determining the importance points on the scattered data that produces a very good reconstructed surface with higher accuracy while maintaining the smoothness of the surface. © Springer Nature Switzerland AG 2020.
Item Type: | Article |
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Additional Information: | cited By 2; Conference of 20th International Conference on Computational Science, ICCS 2020 ; Conference Date: 3 June 2020 Through 5 June 2020; Conference Code:241129 |
Uncontrolled Keywords: | Approximation theory; Functions; Heat conduction; Image segmentation; Interpolation; Linear equations; Radial basis function networks, Approximation methods; Delau-nay triangulations; Numerical computations; Radial basis functions; Reconstructed surfaces; Scientific discovery; System of linear equations; Systems of linear equations, Computational efficiency |
Depositing User: | Mr Ahmad Suhairi UTP |
Date Deposited: | 10 Nov 2023 03:28 |
Last Modified: | 10 Nov 2023 03:28 |
URI: | https://khub.utp.edu.my/scholars/id/eprint/13829 |