Rational Function Interpolation And Approximation

In the paper, we obtain the compact formulae for Hermite interpolation polynomial and Newton-Pade type approximation by the functional C which introduced by Brezinski ([5]) to define Pade type approximation. The algebraic properties of Newton-Pade type approximants (i.e. rational interpolants with prescribed poles) are studied. The connection between the denominator of rational Hermite interpolants and the generalized orthogonal polynomials with respect to the functional C and a class of weight functions determined by knots of interpolation is given.