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On monotone and convex spline interpolation


Author: Paolo Costantini
Journal: Math. Comp. 46 (1986), 203-214
MSC: Primary 65D05; Secondary 41A05, 41A15
DOI: https://doi.org/10.1090/S0025-5718-1986-0815841-7
MathSciNet review: 815841
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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.


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DOI: https://doi.org/10.1090/S0025-5718-1986-0815841-7
Article copyright: © Copyright 1986 American Mathematical Society

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