Comonotone and coconvex rational interpolation and approximation (Q639347)

Let \(x_0,\ldots,x_n\) be given points and \(f_0,\ldots,f_n\) function values. Algorithms for constructing shape-preserving barycentric rational interpolations \[ r_n(x)=\frac{\sum_{i=0}^nf_i\frac{w_i}{x-x_i}}{\sum_{i=0}^n\frac{w_i}{x-x_i}}, \] with suitable \(w_i\) are described. The interpolation of interval data is also considered.