Barycentric Lagrange Blending Rational Interpolation Based on Padé Approximation

The advantages of bar centric interpolation formulations in computation are small number of floating points operations and good numerical stability. Adding a new data pair, the bar centric interpolation formula don't require renew computation of all basis functions. A new kind of blending rational inter polants was constructed by combination of barycentric Lagrange interpolation and Pade approximation. For a given formal power series at every interpolation node, a Pade approximant was made and then they were blended by means of Lagrange's polynomial interpolations to form a new blending rational interpolation-bar centric Lagrange blending rational interpolation based on Pade approximation. Different blending rational inter polants including bar centric Lagrange polynomial interpolation as their special case can be obtained by the new blending rational interpolation method with selecting Pade approximant at each interpolation node. In order to obtain more accurate interpolation, bary centric Lagrange's interpolation based on Pade-type approximation and perturbed Pade approximation were studied. Numerical examples are given to show the validity of the new method.