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 - <p style="text-align: justify;">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.</p>