Pade and Hermite-Pade approximation and orthogonality

Details Pade and Hermite-Pade approximation and orthogonality Pade and Hermite-Pade approximation and orthogonality

2006-09-04

arxiv.org/abs/math/0609094v1

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

Mathematics

Classical Analysis and ODEs

31 pages

Scientific paper

We give a short introduction to Pade approximation (rational approximation to a function with close contact at one point) and to Hermite-Pade 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 Pade and Hermite-Pade approximation.

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