Interpolation rationnelle par méthodes récursives

Abstract

Rational interpolation consists of interpolating a function with a quotient of polynomials. This problem is fundamentally non-linear but one can obtain its solutions by solving a derived linear problem called the Newton-Padé problem. The latter is a generalized Padé problem including conditions at several interpolation points. The recursive methods used to solve the Newton-Padé problem are mainly based on the structure of the Newton-Padé table which collects the solutions of the aforementioned problem. The efficiency of these methods depends largely on the shape of the sets of identical interpolants as the basic idea is to follow a diagonal in the Newton-Padé table. The theoretical study is accompanied with the implementation of an algorithm and the interpretation of the numerical results obtained.

Date of Award	1996
Original language	French
Supervisor	Jean-Pierre Thiran (Supervisor)