A family of multivariate multiquadric quasi-interpolation operators with higher degree polynomial reproduction

作者：Wu Ruifeng; Wu Tieru; Li Huilai^*

来源：Journal of Computational and Applied Mathematics, 2015, 274: 88-108.

DOI：10.1016/j.cam.2014.07.008

• Quasi-interpolation
• Multiquadric functions
• Dimension-splitting
• Lagrange basis functions
• Polynomial reproduction
• Convergence rate

In this paper, by using multivariate divided difference (Rabut, 2001) to approximate the partial derivative and the idea of the superposition (Waldron, 2009), we modify a multiquadric quasi-interpolation operator (Ling, 2004) based on a dimension-splitting technique with the property of linear reproducing to gridded data on multi-dimensional spaces, such that a family of proposed multivariate multiquadric quasi-interpolation operators Phi(r+1) has the property of r + 1 (r is an element of Z, r >= 0) degree polynomial reproducing and converges up to a rate of r + 2. In addition, the proposed quasi-interpolation operator only demands information of location points rather than the derivatives of the function approximated. Moreover, we give the approximation error of our quasi-interpolation operator. Finally, some numerical experiments are shown to confirm the approximation capacity of our quasi-interpolation operator.

• 出版日期2015-1-15
• 单位吉林大学