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Multivariate convexity preserving interpolation by smooth functions

โœ Scribed by J. M. Carnicer

Book ID
112749401
Publisher
Springer
Year
1995
Tongue
English
Weight
419 KB
Volume
3
Category
Article
ISSN
1019-7168

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This paper is concerned with the problem of strict convexity preserving interpolation in one variable. It is shown that a strictly convex Hermite interpolant to strictly convex data can always be chosen smooth and even to be a polynomial. Furthermore, two-point Hermite strict convexity preserving in

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Error bounds between a nonlinear interpolation and the limit function of its associated subdivision scheme are estimated. The bounds can be evaluated without recursive subdivision. We show that this interpolation is convexity preserving, as its associated subdivision scheme. Finally, some numerical