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Fast and reliable high accuracy computation of Gauss--Jacobi quadrature
A. Gil, J. Segura, N. M. Temme
Iterative methods with certified convergence for the computation of Gauss--Jacobi quadratures are described. The methods do not require a priori estimations of the nodes to guarant…
math.NA2020
Numerical evaluation of Airy-type integrals arising in uniform asymptotic analysis
Amparo Gil, Javier Segura, Nico M. Temme
We describe a method to evaluate integrals that arise in the asymptotic analysis when two saddle points may be close together. These integrals, which appear in problems from optics…