Interpolation and Best Approximation for Spherical Radial Basis Function Networks | Zendy

Shao-Bo Lin | Zendy; Jinshan Zeng | Zendy; Zongben Xu | Zendy

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Interpolation and Best Approximation for Spherical Radial Basis Function Networks

Author(s) -

Shao-Bo Lin,

Jinshan Zeng,

Zongben Xu

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/206265

Subject(s) - radial basis function , mathematics , basis (linear algebra) , kernel (algebra) , space (punctuation) , basis function , interpolation (computer graphics) , function (biology) , mathematical analysis , function space , radial basis function network , geometry , pure mathematics , computer science , artificial intelligence , artificial neural network , image (mathematics) , evolutionary biology , biology , operating system

Within the conventional framework of a native space structure, a smooth kernel generates asmall native space, and radial basis functions stemming from the smooth kernel are intended toapproximate only functions from this small native space. In this paper, we embed the smoothradial basis functions in a larger native space generated by a less smooth kernel and use themto interpolate the samples. Our result shows that there exists a linear combination of sphericalradial basis functions that can both exactly interpolate samples generated by functions in thelarger native space and near best approximate the target function

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