A Fast Solution for the Generalized Radial Basis Functions Interpolant
In this paper, we propose a fast solution method of the generalized radial basis functions interpolant for global interpolation. The method can be used to efficiently interpolate large numbers of geometry constraints for implicit surface reconstruction. The basic idea of our approach is based on the...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IEEE
2020-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/9079527/ |
| _version_ | 1830089973538226176 |
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| author | Deyun Zhong Liguan Wang Lin Bi |
| author_facet | Deyun Zhong Liguan Wang Lin Bi |
| author_sort | Deyun Zhong |
| collection | DOAJ |
| description | In this paper, we propose a fast solution method of the generalized radial basis functions interpolant for global interpolation. The method can be used to efficiently interpolate large numbers of geometry constraints for implicit surface reconstruction. The basic idea of our approach is based on the far field expansion of the kernel and the preconditioned Krylov iteration using the domain decomposition method as a preconditioner. We present a fast evaluation method of the matrix-vector product for the linear system. To minimize the number of iterations for large numbers of constraints, the multi-level domain decomposition method is applied to improve overlap using a nested sequence of levels. The implemented solution algorithm generally achieves O(NlogN) complexity and O(N) storage. It is kernel independent both in the evaluation and solution processes without analytical expansions. It is very convenient to apply various types of RBF kernels in different applications without excessive modifications to the existing process. Numerical results show that the fast evaluation method has a good performance for the evaluation of the matrix-vector product and the preconditioned Krylov subspace iterative method has a good convergence rate with a small number of iterations. |
| first_indexed | 2024-12-16T16:54:46Z |
| format | Article |
| id | doaj.art-e24aef0bd218406ca89dad4b43661a0c |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-16T16:54:46Z |
| publishDate | 2020-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-e24aef0bd218406ca89dad4b43661a0c2022-12-21T22:23:55ZengIEEEIEEE Access2169-35362020-01-018801488015910.1109/ACCESS.2020.29907319079527A Fast Solution for the Generalized Radial Basis Functions InterpolantDeyun Zhong0https://orcid.org/0000-0002-1874-4732Liguan Wang1https://orcid.org/0000-0001-8268-9697Lin Bi2https://orcid.org/0000-0002-1652-5122School of Resources and Safety Engineering, Central South University, Changsha, ChinaSchool of Resources and Safety Engineering, Central South University, Changsha, ChinaSchool of Resources and Safety Engineering, Central South University, Changsha, ChinaIn this paper, we propose a fast solution method of the generalized radial basis functions interpolant for global interpolation. The method can be used to efficiently interpolate large numbers of geometry constraints for implicit surface reconstruction. The basic idea of our approach is based on the far field expansion of the kernel and the preconditioned Krylov iteration using the domain decomposition method as a preconditioner. We present a fast evaluation method of the matrix-vector product for the linear system. To minimize the number of iterations for large numbers of constraints, the multi-level domain decomposition method is applied to improve overlap using a nested sequence of levels. The implemented solution algorithm generally achieves O(NlogN) complexity and O(N) storage. It is kernel independent both in the evaluation and solution processes without analytical expansions. It is very convenient to apply various types of RBF kernels in different applications without excessive modifications to the existing process. Numerical results show that the fast evaluation method has a good performance for the evaluation of the matrix-vector product and the preconditioned Krylov subspace iterative method has a good convergence rate with a small number of iterations.https://ieeexplore.ieee.org/document/9079527/Radial basis functionsgeneralized radial basis functionsfar field expansiondomain decomposition methodimplicit surface reconstruction |
| spellingShingle | Deyun Zhong Liguan Wang Lin Bi A Fast Solution for the Generalized Radial Basis Functions Interpolant IEEE Access Radial basis functions generalized radial basis functions far field expansion domain decomposition method implicit surface reconstruction |
| title | A Fast Solution for the Generalized Radial Basis Functions Interpolant |
| title_full | A Fast Solution for the Generalized Radial Basis Functions Interpolant |
| title_fullStr | A Fast Solution for the Generalized Radial Basis Functions Interpolant |
| title_full_unstemmed | A Fast Solution for the Generalized Radial Basis Functions Interpolant |
| title_short | A Fast Solution for the Generalized Radial Basis Functions Interpolant |
| title_sort | fast solution for the generalized radial basis functions interpolant |
| topic | Radial basis functions generalized radial basis functions far field expansion domain decomposition method implicit surface reconstruction |
| url | https://ieeexplore.ieee.org/document/9079527/ |
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