Jaen Journal on Approximation vol:6 issue:2 pages:233-260
We present C^3 or C^4 shape-preserving interpolation schemes based on a two-parameter family of rational quintics, which fits in the frame proposed in [Merrien and Sablonnière, CAGD 30, 2013]. First, given a set of data values and first derivatives, we construct a C^3 shape-preserving piecewise rational quintic interpolant. Second, when only data values are available, a C^4 shape-preserving piecewise rational quintic interpolant is provided. These interpolants are obtained by solving a suitable linear sparse system. We show that it is always possible to select the shape parameters associated with each rational quintic segment so that the shape of the data is locally preserved.