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Spherical scattered data quasi-interpolation by Gaussian radial basis function

Abstract

Since the spherical Gaussian radial function is strictly positive definite, the authors use the linear combinations of translations of the Gaussian kernel to interpolate the scattered data on spheres in this article. Seeing that target functions are usually outside the native spaces, and that one has to solve a large scaled system of linear equations to obtain combinatorial coefficients of interpolant functions, the authors first probe into some problems about interpolation with Gaussian radial functions. Then they construct quasi-interpolation operators by Gaussian radial function, and get the degrees of approximation. Moreover, they show the error relations between quasi-interpolation and interpolation when they have the same basis functions. Finally, the authors discuss the construction and approximation of the quasi-interpolant with a local support function.

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Author information

Correspondence to Zhixiang Chen.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 61272023, 61179041).

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Cite this article

Chen, Z., Cao, F. Spherical scattered data quasi-interpolation by Gaussian radial basis function. Chin. Ann. Math. Ser. B 36, 401–412 (2015). https://doi.org/10.1007/s11401-015-0907-7

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Keywords

  • Scattered data
  • Approximation
  • Spherical Gaussian radial basis function
  • Modulus of continuity

2000 MR Subject Classification

  • 41A17
  • 41A25
  • 41A63