Padé-Faber approximation of Markov functions on real-symmetric compact sets

Study of Padé-Faber approximation (generalization of Padéapproximation and Padé-Chebyshev approximation) of Markov functions is important not only from the point of view of mathematical analysis, but also of computational mathematics. The theorem on the existence of subdiagonal approximants is constructively proved. Various estimates of the approximation error are given. Theoretical assertions are illustrated by simulation results.