Approximation by simple partial fractions and their generalizations

We consider a multiple interpolation by Padé simple partial fractions and propose a method for calculating the values of rational functions and polynomials on the basis of approximation by special rational functions (their numerator and denominator are represented as the differences between two simple partial fractions). We obtain an extrapolation formula for an analytic function h(z) in a neighborhood of the origin. For an extrapolation tool we use the expressions Σ _k λ _k h(λ _k z), where λ _k are calculated by a certain algorithm and are independent of the choice of h. Bibliography: 17 titles.