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The development of theory and algorithms relating to interpolation to data by functions which preserve the monotonicity and/or convexity of the data is presented. The functions used for interpolation are polynomials, piecewise polynomials, polynomial splines and exponential splines. The techniques emphasized are the shape-preserving splines of the author, although some discussion of alternate techniques is given.
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John A. Roulier (1980) studied this question.
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