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Zbl 1174.65315
Tian, Meng; Li, Shilong
Convexity-preserving piecewise rational cubic interpolation. (Chinese. English summary)
[J] J. Shandong Univ., Nat. Sci. 42, No. 10, 80-83,89 (2007). ISSN 1671-9352

Summary: An explicit representation of a $C^1$ piecewise rational cubic spline is developed, which can produce a convex interpolant to given convex data. the explicit representation is easily constructed, and no additional restriction on data is needed. Numerical experiments indicate that the method produces visually pleasing curves. Furthermore, an error analysis of the interpolant is given.

MSC 2000:: *65D07 Splines (numerical methods)
65D05 Interpolation (numerical methods)
41A05 Interpolation
41A15 Spline approximation
41A20 Approximation by rational functions

Keywords: rational cubic spline; interpolation; convexity-preserving; numerical experiments; error analysis

Cited in: Zbl 1227.65016

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