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Volume 25, Issue 2
Radial Basis Function Interpolation in Sobolev Spaces and Its Applications

Manping Zhang

J. Comp. Math., 25 (2007), pp. 201-210.

Published online: 2007-04

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  • Abstract

In this paper we study the method of interpolation by radial basis functions and give some error estimates in Sobolev space $H^k(\Omega)$ $(k \geq 1)$. With a special kind of radial basis function, we construct a basis in $H^k(\Omega)$ and derive a meshless method for solving elliptic partial differential equations. We also propose a method for computing the global data density.

  • Keywords

Sobolev space, Radial basis function, Global data density, Meshless method.

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COPYRIGHT: © Global Science Press

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@Article{JCM-25-201, author = {}, title = {Radial Basis Function Interpolation in Sobolev Spaces and Its Applications}, journal = {Journal of Computational Mathematics}, year = {2007}, volume = {25}, number = {2}, pages = {201--210}, abstract = {

In this paper we study the method of interpolation by radial basis functions and give some error estimates in Sobolev space $H^k(\Omega)$ $(k \geq 1)$. With a special kind of radial basis function, we construct a basis in $H^k(\Omega)$ and derive a meshless method for solving elliptic partial differential equations. We also propose a method for computing the global data density.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8685.html} }
TY - JOUR T1 - Radial Basis Function Interpolation in Sobolev Spaces and Its Applications JO - Journal of Computational Mathematics VL - 2 SP - 201 EP - 210 PY - 2007 DA - 2007/04 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8685.html KW - Sobolev space, Radial basis function, Global data density, Meshless method. AB -

In this paper we study the method of interpolation by radial basis functions and give some error estimates in Sobolev space $H^k(\Omega)$ $(k \geq 1)$. With a special kind of radial basis function, we construct a basis in $H^k(\Omega)$ and derive a meshless method for solving elliptic partial differential equations. We also propose a method for computing the global data density.

Manping Zhang. (1970). Radial Basis Function Interpolation in Sobolev Spaces and Its Applications. Journal of Computational Mathematics. 25 (2). 201-210. doi:
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