Convergence analysis of corner cutting algorithms refining nets of functions

• Published in: Mathematics and computers in simulation Vol. 176; pp. 134 - 146
• Main Authors: Conti, Costanza, Dyn, Nira, Romani, Lucia
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.10.2020
• Subjects: Convergence; Coons transfinite interpolation; Corner cutting for nets of functions; Corner cutting for polygonal lines; Lipschitz continuity; Coons transfinite interpolation; Corner cutting for polygonal lines; Corner cutting for nets of functions; Convergence; Lipschitz continuity
• ISSN: 0378-4754; 1872-7166
• DOI: 10.1016/j.matcom.2020.01.012

In this paper we propose a corner cutting algorithm for nets of functions and prove its convergence using some approximation ideas first applied to the case of corner cutting algorithms refining points with weights proposed by Gregory and Qu. In the net case convergence is proved for the above mentioned weights satisfying an additional condition. The condition requires a bound on the supremum of the relative sizes of the cuts. •We provide a simple convergence proof of corner cutting algorithms refining points.•We extend the corner cutting algorithm to nets of functions.•We show convergence of corner cutting algorithms for bivariate nets of functions.•Both proofs are based on a novel approximation idea.