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Multivariate convexity preserving interpolation by smooth functions

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Abstract

A set of multivariate data is called strictly convex if there exists a strictly convex interpolant to these data. In this paper we characterize strict convexity of Lagrange and Hermite multivariate data by a simple property and show that for strict convex data and given smoothness requirements there exists a smooth strictly convex interpolant. We also show how to construct a multivariate convex smooth interpolant to scattered data.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, Universidad de Zaragoza, E-50009, Zaragoza, Spain

    J. M. Carnicer

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  1. J. M. Carnicer
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Additional information

Communicated by T.N.T. Goodman

Partially supported by DGICYT PS93-0310 and by the EC project CHRX-CT94-0522.

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Carnicer, J.M. Multivariate convexity preserving interpolation by smooth functions. Adv Comput Math 3, 395–404 (1995). https://doi.org/10.1007/BF02432005

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  • DOI: https://doi.org/10.1007/BF02432005

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