ITEM METADATA RECORD
Title: Asymptotic zero distribution of complex orthogonal polynomials associated with Gaussian quadrature
Authors: DeaƱo Cabrera, Alfredo
Huybrechs, Daan
Kuijlaars, Arno
Issue Date: Jan-2010
Publisher: Department of Computer Science, K.U.Leuven
Series Title: TW Reports vol:TW557
Abstract: In this paper we study the asymptotic behavior of a family of polynomials which are orthogonal with respect to an exponential weight on certain contours of the complex plane. The zeros of these polynomials are the nodes for complex Gaussian quadrature of an oscillatory integral on the real axis with a high order stationary point, and their limit distribution is also analyzed. We show that the zeros accumulate along a contour in the complex plane that has the S-property in an external field. In addition, the strong asymptotics of the orthogonal polynomials is obtained by applying the nonlinear Deift-Zhou steepest descent method to the corresponding Riemann-Hilbert problem.
URI: 
Publication status: published
KU Leuven publication type: IR
Appears in Collections:Numerical Analysis and Applied Mathematics Section
Analysis Section

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