Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 41A05, 65D05

Retrieve articles in all journals with MSC: 41A05, 65D05

Additional Information

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