Generalized $C^1$ quadratic B-splines generated by Merrien subdivision algorithm and some applications
数值分析
2025-10-20 v1 数值分析
摘要
A new global basis of B-splines is defined in the space of generalized quadratic splines (GQS) generated by Merrien subdivision algorithm. Then, refinement equations for these B-splines and the associated corner-cutting algorithm are given. Afterwards, several applications are presented. First a global construction of monotonic and/or convex generalized splines interpolating monotonic and/or convex data. Second, convergence of sequences of control polygons to the graph of a GQS. Finally, a Lagrange interpolant and a quasi-interpolant which are exact on the space of affine polynomials and whose infinite norms are uniformly bounded independently of the partition.
引用
@article{arxiv.math/0403380,
title = {Generalized $C^1$ quadratic B-splines generated by Merrien subdivision algorithm and some applications},
author = {Paul Sablonniere},
journal= {arXiv preprint arXiv:math/0403380},
year = {2025}
}
备注
2004-13