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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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 |
| Summary: | 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. |
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| ISSN: | 1734-4492 2353-9003 |