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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…
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…
Fast, reliable and unrestricted iterative computation of Gauss--Hermite and Gauss--Laguerre quadratures
A. Gil, J. Segura, N. M. Temme
Methods for the computation of classical Gaussian quadrature rules are described which are effective both for small and large degree. These methods are reliable because the iterati…
Non-iterative computation of Gauss-Jacobi quadrature
Amparo Gil, Javier Segura, Nico M. Temme
Asymptotic approximations to the zeros of Jacobi polynomials are given, with methods to obtain the coefficients in the expansions. These approximations can be used as standalone me…
Efficient computation of Laguerre polynomials
A. Gil, J. Segura, N. M. Temme
An efficient algorithm and a Fortran 90 module (LaguerrePol) for computing Laguerre polynomials are presented. The standard three-term recurrence relation satisfied…
Efficient algorithms for the inversion of the cumulative central beta distribution
A. Gil, J. Segura, N. M. Temme
Accurate and efficient algorithms for the inversion of the cumulative central beta distribution are described. The algorithms are based on the combination of a fourth-order fixed p…