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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
BELGIUM
E-mail: walter@wis.kuleuven.be
Webpage:
http://www.wis.kuleuven.be/analyse/walter/