Title: Quadratic Hermite-Padé approximation to the exponential function: A Riemann-Hilbert approach
Authors: Kuijlaars, Arno ×
Van Assche, Walter
Wielonsky, Franck #
Issue Date: 2005
Publisher: Springer
Series Title: Constructive approximation vol:21 issue:3 pages:351-412
Abstract: We investigate the asymptotic behavior of the polynomials p, q, r of degrees n in type I Hermite-Pade approximation to the exponential function, defined by p(z)e^{-z} + q(z) + r(z)e^z = O(z^{3n+2}) as z --> 0. These polynomials are characterized by a Riemann-Hilbert problem for a 3 x 3 matrix valued function. We use the Deift-Zhou steepest descent method for Riemann-Hilbert problems to obtain strong uniform asymptotics for the scaled polynomials p(3nz), q(3nz), and r(3nz) in every domain in the complex plane. An important role is played by a three-sheeted Riemann surface and certain measures and functions derived from it. Our work complements the recent results of Herbert Stahl.
ISSN: 0176-4276
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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