Multivariate quasi-interpolation in L~p(R~d) with radial basis functions for scattered data

摘要

In this paper, quasi-interpolation for scattered data was studied. On the basis of generalized quasi-interpolation for scattered data proposed in [Z.M. Wu and J.P. Liu, Generalized strong-fix condition for scattered data quasi-interpolation, Adv. Comput. Math. 23 (2005), pp. 201-214.], we have developed a new method to construct the kernel in the scheme by the linear combination of the scales, instead of the gridded shifts of the radial basis function. Compared with the kernel proposed in [Z.M. Wu and J.P. Liu, Generalized strang-fix condition for scattered data quasi-interpolation, Adv. Comput. Math. 23 (2005), pp. 201-214.], the new kernel, which is still a radial function, possesses the feature of polynomial reproducing property. This opens a possibility for us to propose a different technique by obtaining a higher approximation order of the convergence.