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Shape preserving histopolation using rational quadratic splines. (English) Zbl 0721.65002

The area true approximation of histograms by rational quadratic \(C^ 1\)- splines is considered under constraints like convexity or monotonicity. For the existence of convex or monotone histosplines sufficient and necessary conditions are derived, which always can be satisfied by choosing the rationality parameters appropriately. Since the mentioned problems are in general not uniquely solvable histosplines with minimal mean curvature are constructed.
Reviewer: J.W.Schmidt

MSC:

65D07 Numerical computation using splines
41A15 Spline approximation
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