Product Integration Over Infinite Intervals I. Rules Based on the Zeros of Hermite Polynomials

DOI10.2307/2007528zbMath0542.65013OpenAlexW4252608197MaRDI QIDQ3330384

Alex H. Opie, Ian H. Sloan, William E. Smith

Publication date: 1983

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2007528

zbMATH Keywords

convergencenumerical stabilityoscillatory functionsinfinite intervalsproduct integration ruleszeros of Hermite polynomials

Mathematics Subject Classification ID

Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items (11)

An Analytic and Numerical Analysis of Weighted Singular Cauchy Integrals with Exponential Weights on ℝ ⋮ Géza Freud, orthogonal polynomials and Christoffel functions. A case study ⋮ Approximation of the Hilbert Transform on the real line using Hermite zeros ⋮ A numerical method for solving high-dimensional backward stochastic difference equations using sparse grids ⋮ Mean convergence of Lagrange interpolation for Freud's weights with application to product integration rules ⋮ Suboptimality of Gauss–Hermite Quadrature and Optimality of the Trapezoidal Rule for Functions with Finite Smoothness ⋮ Mean Convergence of Interpolation at Zeros of Airy Functions ⋮ The numerical computation of some integrals on the real line ⋮ Orthogonal Laurent polynomials corresponding to certain strong Stieltjes distributions with applications to numerical quadratures ⋮ Orthogonal Laurent polynomials and quadrature formulas for unbounded intervals. II: interpolatory rules ⋮ Product integration of logarithmic singular integrands based on cubic splines

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