An Analysis of Two Algorithms for Shape-Preserving Cubic Spline Interpolation

1 July 1989

journal article
Published by Oxford University Press (OUP) in IMA Journal of Numerical Analysis

Vol. 9 (3) , 299-314
https://doi.org/10.1093/imanum/9.3.299

Abstract

The use of polynomial splines as a basis for the interpolation of discrete data can be theoretically justified by a minimum principle. It is natural to apply this principle also if shape preserving is added as a constraint, although the construction process is then nonlinear. We discuss two algorithms for the construction of the cubic spline interpolant under the constraint of positivity or monotonicity, and give a detailed convergence analysis. Numerical tests illustrate that analysis.

Keywords

CONVERGENCE ANALYSIS
ALGORITHMS
POLYNOMIAL SPLINES
MONOTONICITY
DISCRETE DATA
MINIMUM PRINCIPLE
SPLINE INTERPOLANT

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