On rational interpolation to \(| x|\) (Q1362769)

For fixed \(n\in \mathbb{N}\) let \(\{x_k^{(n)}\), \(k=1,\dots, n\}\) be a set of distinct interpolation nodes on \((0,1]\), and let \(p_n(x)= \prod_{k=1}^n (x+x_k^{(n)})\), \(r_n(x)=x\cdot \frac{p_n(x)- p_n(-x)} {p_n(x)+ p_n(-x)}\). The authors prove under very weak conditions on the location of the interpolation nodes the convergence of the sequence of the rational interpolants \(r_n(x)\) to \(|x|\) for any real \(x\).