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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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Nonnegativity-, monotonicity-, or convexity-preserving cubic and quintic Hermite interpolation
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by Randall L. Dougherty, Alan S. Edelman and James M. Hyman PDF
Math. Comp. 52 (1989), 471-494 Request permission


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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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Math. Comp. 52 (1989), 471-494
  • MSC: Primary 41A05; Secondary 65D05
  • DOI:
  • MathSciNet review: 962209