Admissible slopes for monotone and convex interpolation |
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Authors: | Alan Edelman Charles A Micchelli |
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Institution: | (1) Department of Mathematics, M.I.T., 02139 Cambridge, MA, USA;(2) Department of Mathematical Sciences, IBM Thomas J. Watson Research Center, P.O. Box 218, 10598 Yorktown Heights, NY, USA |
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Abstract: | 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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Keywords: | AMS(MOS): 65D05 CR: G1 1 |
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