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Constructing radial kernels with higher-order generalized Strang-Fix conditions

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Abstract

The paper provides an approach for constructing multivariate radial kernels satisfying higher-order generalized Strang-Fix conditions from a given univariate generator. There are three key features of the approach. First, the kernels are explicitly expressed only by the derivatives of the f-form of the generator without computing any Fourier transforms. Second, it includes the radial kernels with the highest-order generalized Strang-Fix conditions. Finally, it requires only computing univariate derivatives of the f-form. Therefore, the approach is simple, efficient and easy to implement. As examples, the paper constructs radial kernels from some commonly used generators, including the Gaussian functions, the inverse multiquadric functions and compactly supported positive definite functions.

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Acknowledgments

This work is supported by NSFC (11501006, 61672032), NSFC Key Project (91330201), SGST (12DZ 2272800), Joint Research Fund by National Natural Science Foundation of China and Research Grants Council of Hong Kong (11461161006), Fund of Introducing Leaders of Science and Technology of Anhui University (J10117700057) the 4th Project of Cultivating Backbone of Young Teachers of Anhui University (J01005138), and Anhui Provincial Science and Technology Major Project (16030701091).

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Authors and Affiliations

  1. School of Economics, Anhui University, Hefei, People’s Republic of China

    Wenwu Gao

  2. Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, Shanghai, People’s Republic of China

    Wenwu Gao & Zongmin Wu

  3. Anhui Engineering Laboratory of Agro-Ecological Big Data, Anhui University, Hefei, People’s Republic of China

    Wenwu Gao

  4. Shanghai Center for Mathematical Sciences, Shanghai, People’s Republic of China

    Zongmin Wu

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  1. Wenwu Gao
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Correspondence to Zongmin Wu.

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Communicated by: Tomas Sauer

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Gao, W., Wu, Z. Constructing radial kernels with higher-order generalized Strang-Fix conditions. Adv Comput Math 43, 1355–1375 (2017). https://doi.org/10.1007/s10444-017-9528-x

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