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SAT 2 (2006), 3

Surveys in Approximation Theory, 2 (2006), 61-91.

Padé and Hermite-Padé Approximation and Orthogonality

Walter Van Assche

Abstract. We give a short introduction to Padé approximation (rational approximation to a function with close contact at one point) and to Hermite-Padé approximation (simultaneous rational approximation to several functions with close contact at one point) and show how orthogonality plays a crucial role. We give some insight into how logarithmic potential theory helps in describing the asymptotic behavior and the convergence properties of Padé and Hermite-Padé approximation.

E-print: arXiv:0609094

Published: 1 September 2006.

Walter Van Assche
Katholieke Universiteit Leuven
Department of Mathematics
Celestijnenlaan 200B
B-3001 Leuven