A matrix for determining lower complexity barycentric representations of rational interpolants
Given \(N+1\) nodes \(x_0, x_1, \dots, x_N\) and corresponding values \(f_0, f_1, \dots, f_N\) of a function \(f\) the barycentric rational interpolant of \(f\) is defined by \[ r_N(x)=\frac{\sum_{k=0}^{N}(u_k/(x-x_k))f_k}{\sum_{k=0}^{N}(u_k/(x-x_k))}. \] To remove some numerical disadvantages in computing \(r_N\) the author suggests to diminish the number of interpolation nodes and to compute only \(r_M(x)\) with \(M<N\). He presents an algorithm for computing the weights \(u_k\) and discuss its efficiency with several examples.
scientific article; zbMATH DE number 1534762