Fast, reliable and unrestricted iterative computation of Gauss-Hermite and Gauss-Laguerre quadratures

DOI10.1007/s00211-019-01066-2OpenAlexW2966433303MaRDI QIDQ2334060

Javier Segura, Nico M. Temme, Amparo Gil

Publication date: 6 November 2019

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.05414

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Numerical computation of solutions to single equations (65H05) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Numerical quadrature and cubature formulas (65D32)

Related Items (8)

Fast algorithms using orthogonal polynomials ⋮ A fast and simple algorithm for the computation of the Lerch transcendent ⋮ High-order asymptotic expansions of Gaussian quadrature rules with classical and generalized weight functions ⋮ Asymptotic expansions of Jacobi polynomials and of the nodes and weights of Gauss-Jacobi quadrature for large degree and parameters in terms of elementary functions ⋮ Unnamed Item ⋮ Fast and reliable high-accuracy computation of Gauss-Jacobi quadrature ⋮ Generating the Laguerre expansion coefficients by solving a one-dimensional transport equation ⋮ Exactness of Quadrature Formulas

Uses Software

• LAGUERRE
• FastGaussQuadrature

Cites Work

• Unnamed Item
• Unnamed Item
• Construction and implementation of asymptotic expansions for Jacobi-type orthogonal polynomials
• Sharp bounds for the extreme zeros of classical orthogonal polynomials
• Accurate computation of weights in classical Gauss-Christoffel quadrature rules
• New inequalities from classical Sturm theorems
• Numerically satisfactory solutions of Kummer recurrence relations
• A note on the numerical solution of linear recurrence relations
• Gauss-Radau formulae for Jacobi and Laguerre weight functions
• Global Sturm inequalities for the real zeros of the solutions of the Gauss hypergeometric differential equation
• Generalized Gauss-Radau and Gauss-Lobatto formulae
• Fast computation of Gauss quadrature nodes and weights on the whole real line
• Iteration-Free Computation of Gauss--Legendre Quadrature Nodes and Weights
• $\mathcal{O}(1)$ Computation of Legendre Polynomials and Gauss--Legendre Nodes and Weights for Parallel Computing
• On the Numerical Calculation of the Roots of Special Functions Satisfying Second Order Ordinary Differential Equations
• Reliable Computation of the Zeros of Solutions of Second Order Linear ODEs Using a Fourth Order Method
• Abscissas and weights for Gaussian quadratures of high order
• A Fast Algorithm for the Calculation of the Roots of Special Functions
• Construction and implementation of asymptotic expansions for Laguerre-type orthogonal polynomials
• Fast and Rigorous Arbitrary-Precision Computation of Gauss--Legendre Quadrature Nodes and Weights
• Noniterative Computation of Gauss--Jacobi Quadrature
• Asymptotic Approximations to the Nodes and Weights of Gauss–Hermite and Gauss–Laguerre Quadratures
• On Computing the Points and Weights for Gauss--Legendre Quadrature
• Fast and Accurate Computation of Gauss--Legendre and Gauss--Jacobi Quadrature Nodes and Weights
• Numerical Methods for Special Functions
• Calculation of Gauss Quadrature Rules
• Table of the zeros of the Legendre polynomials of order 1-16 and the weight coefficients for Gauss’ mechanical quadrature formula

This page was built for publication: Fast, reliable and unrestricted iterative computation of Gauss-Hermite and Gauss-Laguerre quadratures