A Muntz type theorem for a family of corner cutting schemes
Dimension elevation process of Gelfond-Bezier curves generates a family of control polygons obtained through a sequence of corner cuttings. 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. (C) 2012 Elsevier B.V. All rights reserved.
corner cutting schemes gelfond-bezier curves bezier curves muntz spaces density of muntz spaces