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Interpolation Method in A Reproducing Kernel Hilbert Space

Lili Yao

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Abstract

In this paper,interpolation function is constructed by basis functions which are presented by the linear combination of a reproducing kernel function in some reproducing kernel Hilbert space.Meanwhile estimation of error and numerical examples are given.As a new method to resolve numerical approximation in the reproducing kernel Hilbert space,it is easy for calculation,better convergent and can be used conveniently.

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What this paper is about

In this paper,interpolation function is constructed by basis functions which are presented by the linear combination of a reproducing kernel function in some reproducing kernel Hilbert space.Meanwhile estimation of error and numerical examples are given.As a new method to resolve numerical approximation in the reproducing kernel Hilbert space,it is easy for calculation,better convergent and can be used conveniently.

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Available abstract

In this paper,interpolation function is constructed by basis functions which are presented by the linear combination of a reproducing kernel function in some reproducing kernel Hilbert space.Meanwhile estimation of error and numerical examples are given.As a new method to resolve numerical approximation in the reproducing kernel Hilbert space,it is easy for calculation,better convergent and can be used conveniently.

Key concepts: Reproducing kernel Hilbert space, Representer theorem, Mathematics, Kernel (algebra), Hilbert space, Interpolation (computer graphics), Kernel embedding of distributions, Applied mathematics

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