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Volume 30, Issue 3
A Multivariate Multiquadric Quasi-Interpolation with Quadric Reproduction

Renzhong Feng & Xun Zhou

DOI: 10.4208/jcm.1111-m3495

J. Comp. Math., 30 (2012), pp. 311-323.

Published online: 2012-06

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  • Abstract

In this paper, by using multivariate divided differences to approximate the partial derivative and superposition, we extend the multivariate quasi-interpolation scheme based on dimension-splitting technique which can reproduce linear polynomials to the scheme quadric polynomials. Furthermore, we give the approximation error of the modified scheme. Our multivariate multiquadric quasi-interpolation scheme only requires information of location points but not that of the derivatives of approximated function. Finally, numerical experiments demonstrate that the approximation rate of our scheme is significantly improved which is consistent with the theoretical results.

  • Keywords

Quasi-interpolation, Multiquadric functions, Polynomial reproduction, $\mathcal{P}_n$-exact A-discretization of $\mathcal{D}^α$, Approximation error.

  • AMS Subject Headings

41A05, 41A25.

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-30-311, author = {Renzhong Feng and Xun Zhou}, title = {A Multivariate Multiquadric Quasi-Interpolation with Quadric Reproduction}, journal = {Journal of Computational Mathematics}, year = {2012}, volume = {30}, number = {3}, pages = {311--323}, abstract = {

In this paper, by using multivariate divided differences to approximate the partial derivative and superposition, we extend the multivariate quasi-interpolation scheme based on dimension-splitting technique which can reproduce linear polynomials to the scheme quadric polynomials. Furthermore, we give the approximation error of the modified scheme. Our multivariate multiquadric quasi-interpolation scheme only requires information of location points but not that of the derivatives of approximated function. Finally, numerical experiments demonstrate that the approximation rate of our scheme is significantly improved which is consistent with the theoretical results.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1111-m3495}, url = {http://global-sci.org/intro/article_detail/jcm/8432.html} }
TY - JOUR T1 - A Multivariate Multiquadric Quasi-Interpolation with Quadric Reproduction AU - Renzhong Feng & Xun Zhou JO - Journal of Computational Mathematics VL - 3 SP - 311 EP - 323 PY - 2012 DA - 2012/06 SN - 30 DO - http://doi.org/10.4208/jcm.1111-m3495 UR - https://global-sci.org/intro/article_detail/jcm/8432.html KW - Quasi-interpolation, Multiquadric functions, Polynomial reproduction, $\mathcal{P}_n$-exact A-discretization of $\mathcal{D}^α$, Approximation error. AB -

In this paper, by using multivariate divided differences to approximate the partial derivative and superposition, we extend the multivariate quasi-interpolation scheme based on dimension-splitting technique which can reproduce linear polynomials to the scheme quadric polynomials. Furthermore, we give the approximation error of the modified scheme. Our multivariate multiquadric quasi-interpolation scheme only requires information of location points but not that of the derivatives of approximated function. Finally, numerical experiments demonstrate that the approximation rate of our scheme is significantly improved which is consistent with the theoretical results.

Renzhong Feng and Xun Zhou. (2012). A Multivariate Multiquadric Quasi-Interpolation with Quadric Reproduction. Journal of Computational Mathematics. 30 (3). 311-323. doi:10.4208/jcm.1111-m3495
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