A Muntz Type Theorem for a Family of Corner Cutting Schemes
Numerical Analysis
2011-12-02 v2
Abstract
By identifying a family of corner cutting schemes as a dimension elevation process of Gelfond-Bezier curves, we give a Muntz type condition for the convergence of the generated control polygons to the underlying curve. The surprising emergence of the Muntz condition in the problem raises the question of a possible connection between the density questions of nested Chebyshev spaces and the convergence of the corresponding dimension elevation algorithms.
Keywords
Cite
@article{arxiv.1111.3410,
title = {A Muntz Type Theorem for a Family of Corner Cutting Schemes},
author = {Rachid Ait-Haddou and Yusuke Sakane and Taishin Nomura},
journal= {arXiv preprint arXiv:1111.3410},
year = {2011}
}
Comments
20 pages, 6 figures. Submitted manuscript v2, corrected typo in formula 2