050 Walter Van Assche
050 Walter Van Assche
Hermite-Padé approximation to two functions with branch points
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Abstract:
Hermite-Padé approximation to two functions is rational approximation to both functions with a common denominator and close contact at one point (we will use infinity). The common denominator is a polynomial with orthogonality conditions for two measures. If the two functions have branch points in the complex plane, then the asymptotic behaviour of the zeros (the poles of the Hermite-Padé approximants) is determined by algebraic functions satisfying a cubic relation.
We will sketch how to get the full asymptotics of the common denominator using the Riemann-Hilbert problem for matrix valued functions for some particular choices of branch points, which appear in applications in number theory.
Rod Halburd | |
54 | |
7/6/2021 | |
00:57:47 | |
CAvid, Complex Analysis |