Residual error based adaptive method with an optimal variable scaling parameter for RBF interpolation
In infinitely smooth Radial Basis Function (RBF) based interpolation, the scaling parameter plays an important role to obtain an accurate and stable numerical solution. When this method is applied to interpolate a function with sharp gradients, then adaptive methods will also play a significant role...
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2023-03-01
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| Series: | International Journal of Applied Mechanics and Engineering |
| Subjects: | |
| Online Access: | https://www.ijame-poland.com/Residual-error-based-adaptive-method-with-an-optimal-variable-scaling-parameter-for,168317,0,2.html |
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| author | G. Krishna Veni Chirala Satyanarayana M. Chenna Krishnareddy |
| author_facet | G. Krishna Veni Chirala Satyanarayana M. Chenna Krishnareddy |
| author_sort | G. Krishna Veni |
| collection | DOAJ |
| description | In infinitely smooth Radial Basis Function (RBF) based interpolation, the scaling parameter plays an important role to obtain an accurate and stable numerical solution. When this method is applied to interpolate a function with sharp gradients, then adaptive methods will also play a significant role in determining an optimal number of centers according to the user desired accuracy. In this article, we test an optimization algorithm developed using the nonlinear optimization to find a scaling parameter for RBF along with an adaptive residual subsampling method [1] RBF interpolation. In this process, at each stage of adoption, the available optimal shape parameters have been obtained by solving the system of non-linear equations. |
| first_indexed | 2024-03-12T16:54:28Z |
| format | Article |
| id | doaj.art-408ca26388e744fcb5b0110e8258f0ce |
| institution | Directory Open Access Journal |
| issn | 1734-4492 2353-9003 |
| language | English |
| last_indexed | 2024-03-12T16:54:28Z |
| publishDate | 2023-03-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | International Journal of Applied Mechanics and Engineering |
| spelling | doaj.art-408ca26388e744fcb5b0110e8258f0ce2023-08-08T10:35:10ZengUniversity of Zielona GóraInternational Journal of Applied Mechanics and Engineering1734-44922353-90032023-03-01281374610.59441/ijame-2023-0004168317Residual error based adaptive method with an optimal variable scaling parameter for RBF interpolationG. Krishna Veni0Chirala Satyanarayana1M. Chenna Krishnareddy2Department of Mathematics, Osmania University College for Women, Hyderabad, INDIADepartment of Mathematics, Ecole Centrale School of Engineering Mahindra University, Hyderabad, INDIADepartment of Mathematics, Osmania University, Hyderabad, INDIAIn infinitely smooth Radial Basis Function (RBF) based interpolation, the scaling parameter plays an important role to obtain an accurate and stable numerical solution. When this method is applied to interpolate a function with sharp gradients, then adaptive methods will also play a significant role in determining an optimal number of centers according to the user desired accuracy. In this article, we test an optimization algorithm developed using the nonlinear optimization to find a scaling parameter for RBF along with an adaptive residual subsampling method [1] RBF interpolation. In this process, at each stage of adoption, the available optimal shape parameters have been obtained by solving the system of non-linear equations.https://www.ijame-poland.com/Residual-error-based-adaptive-method-with-an-optimal-variable-scaling-parameter-for,168317,0,2.htmlradial basis functionadaptive residual subsamplingoptimal shape parameter |
| spellingShingle | G. Krishna Veni Chirala Satyanarayana M. Chenna Krishnareddy Residual error based adaptive method with an optimal variable scaling parameter for RBF interpolation International Journal of Applied Mechanics and Engineering radial basis function adaptive residual subsampling optimal shape parameter |
| title | Residual error based adaptive method with an optimal variable scaling parameter for RBF interpolation |
| title_full | Residual error based adaptive method with an optimal variable scaling parameter for RBF interpolation |
| title_fullStr | Residual error based adaptive method with an optimal variable scaling parameter for RBF interpolation |
| title_full_unstemmed | Residual error based adaptive method with an optimal variable scaling parameter for RBF interpolation |
| title_short | Residual error based adaptive method with an optimal variable scaling parameter for RBF interpolation |
| title_sort | residual error based adaptive method with an optimal variable scaling parameter for rbf interpolation |
| topic | radial basis function adaptive residual subsampling optimal shape parameter |
| url | https://www.ijame-poland.com/Residual-error-based-adaptive-method-with-an-optimal-variable-scaling-parameter-for,168317,0,2.html |
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