Recent advances in shape preserving piecewise cubic interpolation
A number of recent papers have addressed the problem of constructing monotone piecewise cubic interpolants to monotone data. These have focused not only on the monotonicity of the interpolant, but also on properties such as “visual pleasure”, and optimal order error bounds. We review some of these results, and generalize them by constructing C 1 piecewise cubic polynomial interpolants to non-monotone data.These interpolants have a minimum number of changes in sign in the first derivative and approximate an underlying function and its first derivative with optimal order.
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