Title: Type II Hermite-Padé approximation to the exponential function
Authors: Kuijlaars, Arno ×
Stahl, Herbert
Van Assche, Walter
Wielonsky, Franck #
Issue Date: 2007
Publisher: Elsevier
Series Title: Journal of Computational and Applied Mathematics vol:207 pages:227-244
Abstract: We obtain strong and uniform asymptotics in every domain of the complex plane for the scaled polynomials a(3nz), b(3nz), and c(3nz) where a, b, and c are the type II Hermite-Padé approximants to the exponential function of respective degrees 2n+2, 2n and 2n, defined by a(z)e^{-z}-b(z)=O(z^{3n+2}) and a(z)e^{z}-c(z)=O(z^{3n+2}) as z->0. Our analysis relies on a characterization of these polynomials in terms of a 3x3 matrix Riemann-Hilbert problem which, as a consequence of the famous Mahler relations, corresponds by a simple transformation to a similar Riemann-Hilbert problem for type I Hermite-Padé approximants. Due to this relation, the study that was performed in previous work, based on the Deift-Zhou steepest descent method for Riemann-Hilbert problems, can be reused to establish our present results.
ISSN: 0377-0427
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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