Abstract
Following a precise definition of shape-preserving interpolating functions to data, we construct in a new and elementary manner such a cubic spline S 2 ϵ C 2, letting two additional knots per interval. We give an explicit description of S 2, which has satisfactory properties in all the aspects. All the results in the paper—obtained with elementary calculus—are based on the behavior of the derivative of any smooth interpolating function to these data.
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