On monotone and convex spline interpolation

Costantini, Paolo

doi:10.1090/S0025-5718-1986-0815841-7

On monotone and convex spline interpolation
HTML articles powered by AMS MathViewer

by Paolo Costantini PDF

Math. Comp. 46 (1986), 203-214 Request permission

Abstract:

This paper is concerned with the problem of existence of monotone and/or convex splines, having degree n and order of continuity k, which interpolate to a set of data at the knots. The interpolating splines are obtained by using Bernstein polynomials of suitable continuous piecewise linear functions; they satisfy the inequality $k \leqslant n - k$. The theorems presented here are useful in developing algorithms for the construction of shape-preserving splines interpolating arbitrary sets of data points. Earlier results of McAllister, Passow and Roulier can be deduced from those given in this paper.

References

Paolo Costantini, An algorithm for computing shape-preserving interpolating splines of arbitrary degree, J. Comput. Appl. Math. 22 (1988), no. 1, 89–136. MR 948888, DOI 10.1016/0377-0427(88)90290-7
Paolo Costantini and Rossana Morandi, Monotone and convex cubic spline interpolation, Calcolo 21 (1984), no. 3, 281–294 (1985). MR 799625, DOI 10.1007/BF02576538
P. Costantini and R. Morandi, An algorithm for computing shape-preserving cubic spline interpolation to data, Calcolo 21 (1984), no. 4, 295–305 (1985). MR 799994, DOI 10.1007/BF02576168
Rossana Morandi and Paolo Costantini, Piecewise monotone quadratic histosplines, SIAM J. Sci. Statist. Comput. 10 (1989), no. 2, 397–406. MR 982231, DOI 10.1137/0910026
Carl de Boor and Blair Swartz, Piecewise monotone interpolation, J. Approximation Theory 21 (1977), no. 4, 411–416. MR 481727, DOI 10.1016/0021-9045(77)90011-9
G. G. Lorentz, Bernstein polynomials, Mathematical Expositions, No. 8, University of Toronto Press, Toronto, 1953. MR 0057370
David F. McAllister, Eli Passow, and John A. Roulier, Algorithms for computing shape preserving spline interpolations to data, Math. Comp. 31 (1977), no. 139, 717–725. MR 448805, DOI 10.1090/S0025-5718-1977-0448805-0

Shape-Preserving Interpolation by Polynomial Splines

Eli Passow and John A. Roulier, Monotone and convex spline interpolation, SIAM J. Numer. Anal. 14 (1977), no. 5, 904–909. MR 470566, DOI 10.1137/0714060