Convergence analysis of Hermite interpolatory subdivision schemes by explicit joint spectral radius formulas
✍ Scribed by Nicola Guglielmi; Carla Manni; Davide Vitale
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 1022 KB
- Volume
- 434
- Category
- Article
- ISSN
- 0024-3795
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✦ Synopsis
Subdivision schemes are popular iterative processes to build graphs of functions, curves and surfaces. We analyze the 2-point Hermite C 2 subdivision scheme introduced by Merrien in [26]. For the analysis of its convergence and its smoothness properties we are concerned with the computation of the joint spectral radius of a family of 2 matrices associated with the scheme. In this paper, by an explicit computation of the joint spectral radius of such pairs of matrices, we determine necessary and sufficient conditions for the scheme to be C 2 convergent, whenever it reproduces cubic polynomials. In addition, we present two one-parameter families of convergent subdivision schemes belonging to the class in [26] possessing interesting properties from the shape control point of view.