Sharp constants for rational approximations of analytic functions

By Alexander I. Aptekarev. 2002

74 citations recorded by the source corpus.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/9082a0ab9cb6b3c32c6a0293cf07a3afb9f65e57

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In Applied Mathematics

In Numerical Analysis

Citations in the corpus

Strong asymptotics for Jacobi polynomials with varying nonstandard parameters (2003, methodology): “ty on curves in the complex plane. The optimal curves are trajectories of a quadratic diﬀerential and they were used for steepest descent analysis of Riemann-Hilbert problems ﬁrst in [3] and later in [2, 19, 21, 22, 24]. 2 Statement of results 2.1 Geometry of theproblem We assume A and B satisfy the”
Padé approximants for functions with branch points — strong asymptotics of Nuttall–Stahl polynomials (2011, unknown): “It also has been noticed [7, 3, 29, 12] (see also recent paper [13]) that the method works for the non-hermitian orthogonality in the complex plane with respect to complex-valued weights.”
Talbot quadratures and rational approximations (2006, methodology): “A much sharper result than (4.1) was conjectured by Magnus [24] and subsequently proved by Aptekarev [ 1 ]:”
Riemann-Hilbert Analysis for Orthogonal Polynomials (2003, background): “Later developments related to orthogonal polynomials include [2, 3, 5, 18, 20, 21, 22, 23, 34].”
Asymptotic Zero Behavior of Laguerre Polynomials with Negative Parameter (2002, methodology): “Riemann-Hilbert analysis in which a contour selection method was required appeared also in the recent papers [1, 3, 19].”
The AAA Algorithm for Rational Approximation (2016, background): “Probably nobody has a complete view of this terrain, as the developments have occurred in diverse fields including often highly theoretical approximation theory [4, 5, 18, 32, 50, 51, 53, 57, 58, 59, 60, 63, 64], physics [7, 31, 33, 34, 35], systems and control [2, 3, 11, 22, 24, 26, 38, 39, 40, 45,”
Asymptotics of Hermite–Padé Rational Approximants for Two Analytic Functions with Separated Pairs of Branch Points (Case of Genus 0) (2007, methodology): “It has later been noticed [6, 11, 45] that the method also works for the non-Hermitian orthogonality in the complex plane with respect to complex valued weights.”
Critical Measures, Quadratic Differentials, and Weak Limits of Zeros of Stieltjes Polynomials (2009, background): “[4], [24], [47], [49], [50], [64]; this is necessarily a very partial list).”