A Muntz Type Theorem for a Family of Corner Cutting Schemes

Details A Muntz Type Theorem for a Family of Corner Cutting Schemes A Muntz Type Theorem for a Family of Corner Cutting Schemes

2011-11-15

arxiv.org/abs/1111.3410v2

Mathematics

Numerical Analysis

20 pages, 6 figures. Submitted manuscript v2, corrected typo in formula 2

Scientific paper

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.

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