Chebfun and numerical quadrature

DOI10.1007/s11425-012-4474-zzbMath1257.41018OpenAlexW1989097818MaRDI QIDQ1933973

Nicholas Hale, Lloyd N. Threfethen

Publication date: 28 January 2013

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://ora.ox.ac.uk/objects/uuid:1505da1b-1d0e-4038-8128-fb39ac15d65b

zbMATH Keywords

Gauss quadraturefractional calculusRiemann-Liouville integralClenshaw-Curtis quadrature\texttt{Chebfun}barycentric interpolation formula

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Approximate quadratures (41A55) Mathematical software, computer programs (educational aspects) (97N80)

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Uses Software

• Matlab
• Chebfun

Cites Work

• Unnamed Item
• A method for numerical integration on an automatic computer
• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• Doubly adaptive quadrature routines based on Newton-Cotes rules
• Fast construction of the Fejér and Clenshaw-Curtis quadrature rules
• Increasing the Reliability of Adaptive Quadrature Using Explicit Interpolants
• A Fast Algorithm for the Calculation of the Roots of Special Functions
• Barycentric Lagrange Interpolation
• The numerical stability of barycentric Lagrange interpolation
• Fast and Accurate Computation of Gauss--Legendre and Gauss--Jacobi Quadrature Nodes and Weights
• On the convergence rates of Legendre approximation
• Is Gauss Quadrature Better than Clenshaw–Curtis?
• Error Estimation in the Clenshaw-Curtis Quadrature Formula
• Calculation of Gauss Quadrature Rules
• Implementing Clenshaw-Curtis quadrature, I methodology and experience
• Lagrangian Interpolation at the Chebyshev Points xn,     cos (  /n),   = 0(1)n; some Unnoted Advantages

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