Within radial basis functions, handling scale parameters is a well-known and open problem and a proper scaling of the basis function plays a crucial role in applications. A generalization is given in [1] where new transformed kernels based on classical RBFs are defined by using a scale function. In this talk, we show different roles of these variably scaled kernel. In an interpolation process, the variable scale parameter may affect both stability and accuracy and an its appropriate choice can significantly improve the recovery quality. In particular here we discuss their application for the recovery of function with particular features such as discontinuities.
Rossini, M. (2016). Applications of variably scaled kernels. In Multivariate Approximation and Interpolation with Applications (Abstracts) September 19 - 23, 2016 (pp.22-22).
Applications of variably scaled kernels
Rossini, M
2016
Abstract
Within radial basis functions, handling scale parameters is a well-known and open problem and a proper scaling of the basis function plays a crucial role in applications. A generalization is given in [1] where new transformed kernels based on classical RBFs are defined by using a scale function. In this talk, we show different roles of these variably scaled kernel. In an interpolation process, the variable scale parameter may affect both stability and accuracy and an its appropriate choice can significantly improve the recovery quality. In particular here we discuss their application for the recovery of function with particular features such as discontinuities.
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