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Zbl 0617.41015
Costantini, Paolo
On monotone and convex spline interpolation.
(English)
[J] Math. Comput. 46, 203-214 (1986). ISSN 0025-5718; ISSN 1088-6842/e

The author investigates the problem of the existence of monotone and/or convex splines which have degree n and order of continuity k and which interpolate a given set of data. Where they exist, the author gives a method for obtaining the desired splines by using Bernstein polynomials of appropriate piecewise linear functions. A number of algorithms involving the given data are developed which indicate the existence or non-existence of a solution to the problem with appropriate monotone or convex characteristics, or both. In all cases considered, a necessary condition for a solution to exist is that $k\le n-k$. These results generalize results due to {\it D. F. McAllister, E. Passow} and {\it J. A. Roulier} [Math. Comput. 31, 717-725 (1977; Zbl 0371.65001)] and {\it E. Passow} and {\it J. A. Roulier} [SIAM J. Numer. Anal. 14, 904-909 (1977; Zbl 0378.41002)].
[P.Lappan]
MSC 2000:
*41A15 Spline approximation

Keywords: monotone spline; convex splines; Bernstein polynomials

Citations: Zbl 0371.65001; Zbl 0378.41002

Cited in: Zbl 0646.65009

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