A kind of multiquadric quasi-interpolation operator satisfying any degree polynomial reproduction property to scattered data

作者：Feng Renzhong^*; Zhou Xun

来源：Journal of Computational and Applied Mathematics, 2011, 235(5): 1502-1514.

DOI：10.1016/j.cam.2010.08.037

• Quasi-interpolation
• Scattered data
• Multiquadric function
• Polynomial reproducing
• Approximation rate

In this paper, by virtue of using the linear combinations of the shifts off (x) to approximate the derivatives of f (x) and Waldron's superposition idea (2009). we modify a multiquadric quasi-interpolation with the property of linear reproducing to scattered data on one-dimensional space, such that a kind of quasi-interpolation operator Lr+1f has the property of r + 1(r epsilon Z. r >= 0) degree polynomial reproducing and converges up to a rate of r + 2. There is no demand for the derivatives off in the proposed quasi-interpolation Lr+1f, so it does not increase the orders of smoothness of f. Finally, some numerical experiments are shown to compare the approximation capacity of our quasi-interpolation operators with that of Wu-Schaback's quasi-interpolation scheme and Feng-Li's quasi-interpolation scheme.

• 出版日期2011-1-1
• 单位北京航空航天大学