Residual error based adaptive method with an optimal variable scaling parameter for RBF interpolation
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Department of Mathematics, Osmania University College for Women, Hyderabad, INDIA
Department of Mathematics, Ecole Centrale School of Engineering Mahindra University, Hyderabad, INDIA
Department of Mathematics, Osmania University, Hyderabad, INDIA
Publication date: 2023-03-01
Corresponding author
Chirala Satyanarayana
International Journal of Applied Mechanics and Engineering 2023;28(1):37-46
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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