4 papers
Fast and accurate computation of classical Gaussian quadratures
A. Gil, J. Segura, N. M. Temme
Algorithms for computing the classical Gaussian quadrature rules (Gauss--Jacobi, Gauss--Laguerre, and Gauss--Hermite) are presented, based on globally convergent fourth-order itera…
Computation of parabolic cylinder functions having complex argument
T. M. Dunster, A. Gil, J. Segura
Numerical methods for the computation of the parabolic cylinder for real and complex are presented. The main tools are recent asymptotic expansions involving expon…
Asymptotic inversion of the binomial and negative binomial cumulative distribution functions
A. Gil, J. Segura, N. M. Temme
The computation and inversion of the binomial and negative binomial cumulative distribution functions play a key role in many applications. In this paper, we explain how methods us…
Simplified error bounds for turning point expansions
T. M. Dunster, A. Gil, J. Segura
Recently, the present authors derived new asymptotic expansions for linear differential equations having a simple turning point. These involve Airy functions and slowly varying coe…