Properties of generators of quasi-interpolation operators of high approximation orders in spaces of polyharmonic splines

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:267

Article

Bozzini, Mira¹  Rossini, Milvia¹ 

[1] Univ Milano Bicocca, Milan, Italy

关键词: Polyharmonic splines;    Quasi-interpolation operators;    High degree polynomial reproduction;    Multiresolution analysis;    Scaling functions;    Subdivision;   

DOI  :  10.1016/j.cam.2014.01.029

来源: Elsevier

【 摘 要 】

We have presented in Bozzini et al. (2011) a procedure in spaces of m-harmonic splines in R-d that starts from a simple generator phi(0) and recursively defines generators phi(1), phi(2),..., phi(m-1) with corresponding quasi-interpolation operators reproducing polynomials of degrees 3, 5,..., 2m - 1 respectively. In this paper we study the properties of generators phi(j), and we prove that these new generators are positive definite functions, and are scaling functions whenever phi(0) has those properties. Moreover phi(0) and phi(j) generate the same multiresolution analysis. We show that it is possible to define a convergent subdivision scheme, and to provide in this way a fast computation of the quasi-interpolant. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free