Computation of Fourier transform integrals using Chebyshev series expansions

DOI10.1007/BF02253692zbMath0514.65098OpenAlexW90875409MaRDI QIDQ1051411

Robert Piessens, Maria Branders

Publication date: 1984

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02253692

zbMATH Keywords

Fourier transformnumerical examplesnumerical stabilityChebyshev series approximationlinear four-terms recurrence relation

Mathematics Subject Classification ID

Numerical methods for integral transforms (65R10) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Numerical methods for trigonometric approximation and interpolation (65T40)

Related Items (11)

A well-conditioned Levin method for calculation of highly oscillatory integrals and its application ⋮ Filon-Clenshaw-Curtis formulas for highly oscillatory integrals in the presence of stationary points ⋮ Unnamed Item ⋮ On fast and stable implementation of Clenshaw-Curtis and Fejér-type quadrature rules ⋮ On the computation of Fourier transforms of singular functions ⋮ Efficient calculation and asymptotic expansions of many different oscillatory infinite integrals ⋮ A sparse fractional Jacobi-Galerkin-Levin quadrature rule for highly oscillatory integrals ⋮ Modified filon-Clenshaw-Curtis rules for oscillatory integrals with a nonlinear oscillator ⋮ Spectral Levin-type methods for calculation of generalized Fourier transforms ⋮ Computing integral transforms and solving integral equations using Chebyshev polynomial approximations ⋮ On error bounds of Filon-Clenshaw-Curtis quadrature for highly oscillatory integrals

Uses Software

• QUADPACK

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A method for numerical integration on an automatic computer
• An extension of Clenshaw-Curtis quadrature
• Construction of cubature formulas of degree eleven for symmetric planar regions, using orthogonal polynomials
• The numerical solution of linear recurrence relations

This page was built for publication: Computation of Fourier transform integrals using Chebyshev series expansions