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Nonnegativity-, monotonicity-, or convexity-preserving cubic and quintic Hermite interpolation

Authors: Randall L. Dougherty, Alan S. Edelman and James M. Hyman
Journal: Math. Comp. 52 (1989), 471-494
MSC: Primary 41A05; Secondary 65D05
MathSciNet review: 962209
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Abstract: The Hermite polynomials are simple, effective interpolants of discrete data. These interpolants can preserve local positivity, monotonicity, and convexity of the data if we restrict their derivatives to satisfy constraints at the data points. This paper describes the conditions that must be satisfied for cubic and quintic Hermite interpolants to preserve these properties when they exist in the discrete data. We construct algorithms to ensure that these constraints are satisfied and give numerical examples to illustrate the effectiveness of the algorithms on locally smooth and rough data.

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Keywords: Approximation theory, convexity, interpolation, monotonicity, shape preservation, spline
Article copyright: © Copyright 1989 American Mathematical Society

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