Numerical evaluation of the \(p\)th derivative of Jacobi series

DOI10.1016/S0168-9274(02)00106-XzbMath1018.65031MaRDI QIDQ1861986

Juan Manuel Peña, Roberto Barrio

Publication date: 10 March 2003

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

zbMATH Keywords

algorithmChebyshev polynomialsJacobi polynomialspseudospectral methodsLegendre polynomialrounding errorsultraspherical polynomialderivative evaluation

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Computation of special functions and constants, construction of tables (65D20) Numerical differentiation (65D25) Numerical approximation and evaluation of special functions (33F05)

Related Items (10)

Basis conversions among univariate polynomial representations ⋮ Computing Derivatives of Jacobi Polynomials Using Bernstein Transformation and Differentiation Matrix ⋮ Algorithms for the integration and derivation of Chebyshev series. ⋮ Accurate Computations and Applications of Some Classes of Matrices ⋮ Generation and evaluation of orthogonal polynomials in discrete Sobolev spaces. I: Algorithms ⋮ Generation and evaluation of orthogonal polynomials in discrete Sobolev spaces. II: numerical stability ⋮ Three term recurrence for the evaluation of multivariate orthogonal polynomials ⋮ Evaluation of the derivative of a polynomial in Bernstein form ⋮ Higher order pseudospectral differentiation matrices ⋮ \textsf{ORTHOPOLY}: a library for accurate evaluation of series of classical orthogonal polynomials and their derivatives

Uses Software

• mctoolbox
• Differentiation Matrix Suite
• splib

Cites Work

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