Summary
In many applications, interpolation of experimental data exhibiting some geometric property such as nonnegativity, monotonicity or convexity is unacceptable unless the interpolant reflects these characteristics. This paper identifies admissible slopes at data points of variousC 1 interpolants which ensure a desirable shape. We discuss this question, in turn for the following function classes commonly used for shape preserving interpolations: monotone polynomials,C 1 monotone piecewise polynomials, convex polynomials, parametric cubic curves and rational functions.
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References
Fritsch, F.N., Carlson, R.E.: Monotone piecewise cubic interpolation. SIAM J. Numer. Anal.17, 238–246 (1980)
Gregory, J.A., Delbourgo, R.: Piecewise rational quadratic interpolation to monotonic data. IMA J. Numer. Anal.2, 123–130 (1982)
Hyman, J.M.: Accurate monotonicity preserving cubic interpolation. SIAM J. Sci. Stat. Comput.4, 645–654 (1983)
Karlin, S., Studden, W.J.: Tchebycheff systems: with applications in analysis and statistics. New York: Interscience Publishers 1966
Schumaker, L.L.: On shape preserving quadratic spline interpolation. SIAM J. Numer. Anal.20, 854–864 (1983)
Szegö, G.: Orthogonal polynomials. American Mathematical Society. Providence, R.I. 1939
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Edelman, A., Micchelli, C.A. Admissible slopes for monotone and convex interpolation. Numer. Math. 51, 441–458 (1987). https://doi.org/10.1007/BF01397546
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DOI: https://doi.org/10.1007/BF01397546