A new formal approach to the rational interpolation problem.
A powerful determinant.
Absolute Monotonicity of Rational Functions Occurring in the Numerical Solution of Initial Value Problems.
Accelerating the Convergence of a Table with Multiple Entry
An extension to rational functions of a theorem of J. L. Walsh on differences of interpolating polynomials
An intoduction to formal orthogonality and some of its applications.
This paper is an introduction to formal orthogonal polynomials and their application to Padé approximation, Krylov subspace methods for the solution of systems of linear equations, and convergence acceleration methods. Some more general formal orthogonal polynomials, and the concept of biorthogonality and its applications are also discussed.
Approximants de Padé des fonctions binômes et mesures de l'irrationalité des racines de nombres rationnels
Approximants de Padé et -dérivation
Approximants de Padé-Hermite. 1ère partie: théorie.
Approximants de Padé-Hermite. 2ème partie: programmation.
Asymptotics for quadratic Hermite-Padé polynomials associated with the exponential function.
Asymptotics for the nth-degree Laguerre polynomial evaluated at n.
Avoiding look-ahead in the Lanczos method and Padé approximation
In the non-normal case, it is possible to use various look-ahead strategies for computing the elements of a family of regular orthogonal polynomials. These strategies consist in jumping over non-existing and singular orthogonal polynomials by solving triangular linear systems. We show how to avoid them by using a new method called ALA (Avoiding Look-Ahead), for which we give three principal implementations. The application of ALA to Padé approximation, extrapolation methods and Lanczos method for...