Year: 2012
Journal of Computational Mathematics, Vol. 30 (2012), Iss. 3 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1111-m3495
Journal of Computational Mathematics, Vol. 30 (2012), Iss. 3 : pp. 311–323
Published online: 2012-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Quasi-interpolation Multiquadric functions Polynomial reproduction $\mathcal{P}_n$-exact A-discretization of $\mathcal{D}^α$ Approximation error.
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