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Convexity-preserving piecewise rational cubic interpolation. (Chinese) Zbl 1174.65315
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:
65D07Splines (numerical methods)
65D05Interpolation (numerical methods)
41A05Interpolation (approximations and expansions)
41A15Spline approximation
41A20Approximation by rational functions