ARBF: adaptive radial basis function interpolation algorithm for irregularly scattered point sets
Abstract Radial basis functions (RBFs) are isotropic, simple in form, dimensionally independent and mesh-free and are suitable for interpolation and fitting of scattered data. In a scattered point set, the calculation accuracy of multiquadric (MQ) RBF interpolation is strongly related to the selecti...
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| Autor*in: |
Gao, Kaifeng [verfasserIn] Mei, Gang [verfasserIn] Cuomo, Salvatore [verfasserIn] Piccialli, Francesco [verfasserIn] Xu, Nengxiong [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2020 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Soft Computing - Springer-Verlag, 2003, 24(2020), 23 vom: 30. Juli, Seite 17693-17704 |
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| Übergeordnetes Werk: |
volume:24 ; year:2020 ; number:23 ; day:30 ; month:07 ; pages:17693-17704 |
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| DOI / URN: |
10.1007/s00500-020-05211-0 |
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| 520 | |a Abstract Radial basis functions (RBFs) are isotropic, simple in form, dimensionally independent and mesh-free and are suitable for interpolation and fitting of scattered data. In a scattered point set, the calculation accuracy of multiquadric (MQ) RBF interpolation is strongly related to the selection of the shape factor. There is still no uniform method for determining the shape factor. Many scholars focus on determining the single optimal shape factor and seldom consider the change in the shape factor with the spatial point density in scattered point sets. In this paper, an adaptive radial basis function (ARBF) interpolation algorithm is proposed. The shape factors of MQ functions are determined adaptively by the local point densities of the points to be interpolated. To evaluate the computational performance of the ARBF interpolation algorithm, twelve groups of benchmark tests are conducted in this paper. We found that (1) the numerical error of ARBF interpolation is approximately 10% less than that of commonly used RBF interpolation with the shape factor recommended by Hardy. (2) The computational efficiency of ARBF interpolation is 1–2.5% lower than that of commonly used RBF interpolation with the shape factor recommended by Hardy. | ||
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| 650 | 4 | |a Scattered point sets |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Shape factor |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Point density |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Mei, Gang |e verfasserin |4 aut | |
| 700 | 1 | |a Cuomo, Salvatore |e verfasserin |4 aut | |
| 700 | 1 | |a Piccialli, Francesco |e verfasserin |4 aut | |
| 700 | 1 | |a Xu, Nengxiong |e verfasserin |4 aut | |
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10.1007/s00500-020-05211-0 doi (DE-627)SPR041927168 (SPR)s00500-020-05211-0-e DE-627 ger DE-627 rakwb eng Gao, Kaifeng verfasserin aut ARBF: adaptive radial basis function interpolation algorithm for irregularly scattered point sets 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Radial basis functions (RBFs) are isotropic, simple in form, dimensionally independent and mesh-free and are suitable for interpolation and fitting of scattered data. In a scattered point set, the calculation accuracy of multiquadric (MQ) RBF interpolation is strongly related to the selection of the shape factor. There is still no uniform method for determining the shape factor. Many scholars focus on determining the single optimal shape factor and seldom consider the change in the shape factor with the spatial point density in scattered point sets. In this paper, an adaptive radial basis function (ARBF) interpolation algorithm is proposed. The shape factors of MQ functions are determined adaptively by the local point densities of the points to be interpolated. To evaluate the computational performance of the ARBF interpolation algorithm, twelve groups of benchmark tests are conducted in this paper. We found that (1) the numerical error of ARBF interpolation is approximately 10% less than that of commonly used RBF interpolation with the shape factor recommended by Hardy. (2) The computational efficiency of ARBF interpolation is 1–2.5% lower than that of commonly used RBF interpolation with the shape factor recommended by Hardy. RBF interpolation (dpeaa)DE-He213 Scattered point sets (dpeaa)DE-He213 Shape factor (dpeaa)DE-He213 Point density (dpeaa)DE-He213 Mei, Gang verfasserin aut Cuomo, Salvatore verfasserin aut Piccialli, Francesco verfasserin aut Xu, Nengxiong verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 24(2020), 23 vom: 30. Juli, Seite 17693-17704 (DE-627)SPR006469531 nnns volume:24 year:2020 number:23 day:30 month:07 pages:17693-17704 https://dx.doi.org/10.1007/s00500-020-05211-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 24 2020 23 30 07 17693-17704 |
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10.1007/s00500-020-05211-0 doi (DE-627)SPR041927168 (SPR)s00500-020-05211-0-e DE-627 ger DE-627 rakwb eng Gao, Kaifeng verfasserin aut ARBF: adaptive radial basis function interpolation algorithm for irregularly scattered point sets 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Radial basis functions (RBFs) are isotropic, simple in form, dimensionally independent and mesh-free and are suitable for interpolation and fitting of scattered data. In a scattered point set, the calculation accuracy of multiquadric (MQ) RBF interpolation is strongly related to the selection of the shape factor. There is still no uniform method for determining the shape factor. Many scholars focus on determining the single optimal shape factor and seldom consider the change in the shape factor with the spatial point density in scattered point sets. In this paper, an adaptive radial basis function (ARBF) interpolation algorithm is proposed. The shape factors of MQ functions are determined adaptively by the local point densities of the points to be interpolated. To evaluate the computational performance of the ARBF interpolation algorithm, twelve groups of benchmark tests are conducted in this paper. We found that (1) the numerical error of ARBF interpolation is approximately 10% less than that of commonly used RBF interpolation with the shape factor recommended by Hardy. (2) The computational efficiency of ARBF interpolation is 1–2.5% lower than that of commonly used RBF interpolation with the shape factor recommended by Hardy. RBF interpolation (dpeaa)DE-He213 Scattered point sets (dpeaa)DE-He213 Shape factor (dpeaa)DE-He213 Point density (dpeaa)DE-He213 Mei, Gang verfasserin aut Cuomo, Salvatore verfasserin aut Piccialli, Francesco verfasserin aut Xu, Nengxiong verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 24(2020), 23 vom: 30. Juli, Seite 17693-17704 (DE-627)SPR006469531 nnns volume:24 year:2020 number:23 day:30 month:07 pages:17693-17704 https://dx.doi.org/10.1007/s00500-020-05211-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 24 2020 23 30 07 17693-17704 |
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10.1007/s00500-020-05211-0 doi (DE-627)SPR041927168 (SPR)s00500-020-05211-0-e DE-627 ger DE-627 rakwb eng Gao, Kaifeng verfasserin aut ARBF: adaptive radial basis function interpolation algorithm for irregularly scattered point sets 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Radial basis functions (RBFs) are isotropic, simple in form, dimensionally independent and mesh-free and are suitable for interpolation and fitting of scattered data. In a scattered point set, the calculation accuracy of multiquadric (MQ) RBF interpolation is strongly related to the selection of the shape factor. There is still no uniform method for determining the shape factor. Many scholars focus on determining the single optimal shape factor and seldom consider the change in the shape factor with the spatial point density in scattered point sets. In this paper, an adaptive radial basis function (ARBF) interpolation algorithm is proposed. The shape factors of MQ functions are determined adaptively by the local point densities of the points to be interpolated. To evaluate the computational performance of the ARBF interpolation algorithm, twelve groups of benchmark tests are conducted in this paper. We found that (1) the numerical error of ARBF interpolation is approximately 10% less than that of commonly used RBF interpolation with the shape factor recommended by Hardy. (2) The computational efficiency of ARBF interpolation is 1–2.5% lower than that of commonly used RBF interpolation with the shape factor recommended by Hardy. RBF interpolation (dpeaa)DE-He213 Scattered point sets (dpeaa)DE-He213 Shape factor (dpeaa)DE-He213 Point density (dpeaa)DE-He213 Mei, Gang verfasserin aut Cuomo, Salvatore verfasserin aut Piccialli, Francesco verfasserin aut Xu, Nengxiong verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 24(2020), 23 vom: 30. Juli, Seite 17693-17704 (DE-627)SPR006469531 nnns volume:24 year:2020 number:23 day:30 month:07 pages:17693-17704 https://dx.doi.org/10.1007/s00500-020-05211-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 24 2020 23 30 07 17693-17704 |
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10.1007/s00500-020-05211-0 doi (DE-627)SPR041927168 (SPR)s00500-020-05211-0-e DE-627 ger DE-627 rakwb eng Gao, Kaifeng verfasserin aut ARBF: adaptive radial basis function interpolation algorithm for irregularly scattered point sets 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Radial basis functions (RBFs) are isotropic, simple in form, dimensionally independent and mesh-free and are suitable for interpolation and fitting of scattered data. In a scattered point set, the calculation accuracy of multiquadric (MQ) RBF interpolation is strongly related to the selection of the shape factor. There is still no uniform method for determining the shape factor. Many scholars focus on determining the single optimal shape factor and seldom consider the change in the shape factor with the spatial point density in scattered point sets. In this paper, an adaptive radial basis function (ARBF) interpolation algorithm is proposed. The shape factors of MQ functions are determined adaptively by the local point densities of the points to be interpolated. To evaluate the computational performance of the ARBF interpolation algorithm, twelve groups of benchmark tests are conducted in this paper. We found that (1) the numerical error of ARBF interpolation is approximately 10% less than that of commonly used RBF interpolation with the shape factor recommended by Hardy. (2) The computational efficiency of ARBF interpolation is 1–2.5% lower than that of commonly used RBF interpolation with the shape factor recommended by Hardy. RBF interpolation (dpeaa)DE-He213 Scattered point sets (dpeaa)DE-He213 Shape factor (dpeaa)DE-He213 Point density (dpeaa)DE-He213 Mei, Gang verfasserin aut Cuomo, Salvatore verfasserin aut Piccialli, Francesco verfasserin aut Xu, Nengxiong verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 24(2020), 23 vom: 30. Juli, Seite 17693-17704 (DE-627)SPR006469531 nnns volume:24 year:2020 number:23 day:30 month:07 pages:17693-17704 https://dx.doi.org/10.1007/s00500-020-05211-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 24 2020 23 30 07 17693-17704 |
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10.1007/s00500-020-05211-0 doi (DE-627)SPR041927168 (SPR)s00500-020-05211-0-e DE-627 ger DE-627 rakwb eng Gao, Kaifeng verfasserin aut ARBF: adaptive radial basis function interpolation algorithm for irregularly scattered point sets 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Radial basis functions (RBFs) are isotropic, simple in form, dimensionally independent and mesh-free and are suitable for interpolation and fitting of scattered data. In a scattered point set, the calculation accuracy of multiquadric (MQ) RBF interpolation is strongly related to the selection of the shape factor. There is still no uniform method for determining the shape factor. Many scholars focus on determining the single optimal shape factor and seldom consider the change in the shape factor with the spatial point density in scattered point sets. In this paper, an adaptive radial basis function (ARBF) interpolation algorithm is proposed. The shape factors of MQ functions are determined adaptively by the local point densities of the points to be interpolated. To evaluate the computational performance of the ARBF interpolation algorithm, twelve groups of benchmark tests are conducted in this paper. We found that (1) the numerical error of ARBF interpolation is approximately 10% less than that of commonly used RBF interpolation with the shape factor recommended by Hardy. (2) The computational efficiency of ARBF interpolation is 1–2.5% lower than that of commonly used RBF interpolation with the shape factor recommended by Hardy. RBF interpolation (dpeaa)DE-He213 Scattered point sets (dpeaa)DE-He213 Shape factor (dpeaa)DE-He213 Point density (dpeaa)DE-He213 Mei, Gang verfasserin aut Cuomo, Salvatore verfasserin aut Piccialli, Francesco verfasserin aut Xu, Nengxiong verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 24(2020), 23 vom: 30. Juli, Seite 17693-17704 (DE-627)SPR006469531 nnns volume:24 year:2020 number:23 day:30 month:07 pages:17693-17704 https://dx.doi.org/10.1007/s00500-020-05211-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 24 2020 23 30 07 17693-17704 |
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Abstract Radial basis functions (RBFs) are isotropic, simple in form, dimensionally independent and mesh-free and are suitable for interpolation and fitting of scattered data. In a scattered point set, the calculation accuracy of multiquadric (MQ) RBF interpolation is strongly related to the selection of the shape factor. There is still no uniform method for determining the shape factor. Many scholars focus on determining the single optimal shape factor and seldom consider the change in the shape factor with the spatial point density in scattered point sets. In this paper, an adaptive radial basis function (ARBF) interpolation algorithm is proposed. The shape factors of MQ functions are determined adaptively by the local point densities of the points to be interpolated. To evaluate the computational performance of the ARBF interpolation algorithm, twelve groups of benchmark tests are conducted in this paper. We found that (1) the numerical error of ARBF interpolation is approximately 10% less than that of commonly used RBF interpolation with the shape factor recommended by Hardy. (2) The computational efficiency of ARBF interpolation is 1–2.5% lower than that of commonly used RBF interpolation with the shape factor recommended by Hardy. |
| abstractGer |
Abstract Radial basis functions (RBFs) are isotropic, simple in form, dimensionally independent and mesh-free and are suitable for interpolation and fitting of scattered data. In a scattered point set, the calculation accuracy of multiquadric (MQ) RBF interpolation is strongly related to the selection of the shape factor. There is still no uniform method for determining the shape factor. Many scholars focus on determining the single optimal shape factor and seldom consider the change in the shape factor with the spatial point density in scattered point sets. In this paper, an adaptive radial basis function (ARBF) interpolation algorithm is proposed. The shape factors of MQ functions are determined adaptively by the local point densities of the points to be interpolated. To evaluate the computational performance of the ARBF interpolation algorithm, twelve groups of benchmark tests are conducted in this paper. We found that (1) the numerical error of ARBF interpolation is approximately 10% less than that of commonly used RBF interpolation with the shape factor recommended by Hardy. (2) The computational efficiency of ARBF interpolation is 1–2.5% lower than that of commonly used RBF interpolation with the shape factor recommended by Hardy. |
| abstract_unstemmed |
Abstract Radial basis functions (RBFs) are isotropic, simple in form, dimensionally independent and mesh-free and are suitable for interpolation and fitting of scattered data. In a scattered point set, the calculation accuracy of multiquadric (MQ) RBF interpolation is strongly related to the selection of the shape factor. There is still no uniform method for determining the shape factor. Many scholars focus on determining the single optimal shape factor and seldom consider the change in the shape factor with the spatial point density in scattered point sets. In this paper, an adaptive radial basis function (ARBF) interpolation algorithm is proposed. The shape factors of MQ functions are determined adaptively by the local point densities of the points to be interpolated. To evaluate the computational performance of the ARBF interpolation algorithm, twelve groups of benchmark tests are conducted in this paper. We found that (1) the numerical error of ARBF interpolation is approximately 10% less than that of commonly used RBF interpolation with the shape factor recommended by Hardy. (2) The computational efficiency of ARBF interpolation is 1–2.5% lower than that of commonly used RBF interpolation with the shape factor recommended by Hardy. |
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ARBF: adaptive radial basis function interpolation algorithm for irregularly scattered point sets |
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https://dx.doi.org/10.1007/s00500-020-05211-0 |
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Mei, Gang Cuomo, Salvatore Piccialli, Francesco Xu, Nengxiong |
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Mei, Gang Cuomo, Salvatore Piccialli, Francesco Xu, Nengxiong |
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| doi_str |
10.1007/s00500-020-05211-0 |
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2024-07-04T00:11:17.069Z |
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