A fast and simple algorithm for the computation of Legendre coefficients

DOI10.1007/s00211-010-0352-1zbMath1211.33001OpenAlexW1976782593MaRDI QIDQ629903

Arieh Iserles

Publication date: 10 March 2011

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

Full work available at URL: https://doi.org/10.1007/s00211-010-0352-1

zbMATH Keywords

fast Fourier transformhypergeometric functionLegendre polynomialsCauchy theoremalgorithm analytic functiontruncated Taylor expansion

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Approximation in the complex plane (30E10) Numerical methods for discrete and fast Fourier transforms (65T50) Elliptic functions and integrals (33E05) Software, source code, etc. for problems pertaining to special functions (33-04)

Related Items (14)

Model order reduction of MIMO bilinear systems by multi-order Arnoldi method ⋮ Reconstruction of sparse Legendre and Gegenbauer expansions ⋮ Fast algorithms for the multi-dimensional Jacobi polynomial transform ⋮ A matrix method for fractional Sturm-Liouville problems on bounded domain ⋮ On expansions in orthogonal polynomials ⋮ On the convergence rates of Legendre approximation ⋮ A Hybrid Analytical-Numerical Technique for Elliptic PDEs ⋮ Fast polynomial transforms based on Toeplitz and Hankel matrices ⋮ Arnoldi-based model order reduction for linear systems with inhomogeneous initial conditions ⋮ Rapidly computing sparse Legendre expansions via sparse Fourier transforms ⋮ How much faster does the best polynomial approximation converge than Legendre projection? ⋮ On the Optimal Estimates and Comparison of Gegenbauer Expansion Coefficients ⋮ Preconditioned Legendre spectral Galerkin methods for the non-separable elliptic equation ⋮ Dimension reduction for k-power bilinear systems using orthogonal polynomials and Arnoldi algorithm

Cites Work

• Accuracy and stability of computing high-order derivatives of analytic functions by Cauchy integrals
• A Fast Algorithm for the Evaluation of Legendre Expansions
• Fast algorithms for discrete polynomial transforms
• The spectral problem for a class of highly oscillatory Fredholm integral operators
• Is Gauss Quadrature Better than Clenshaw–Curtis?
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