Rounding error bounds for the Clenshaw and Forsythe algorithms for the evaluation of orthogonal polynomial series

DOI10.1016/S0377-0427(01)00382-XzbMath0998.65033MaRDI QIDQ5957927

Roberto Barrio

Publication date: 15 November 2002

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

numerical testsChebyshev and Legendre seriesevaluation of polynomialsGegenbauer seriesorthogonal polynomial seriesrounding error bounds

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Roundoff error (65G50) Computation of special functions and constants, construction of tables (65D20)

Related Items (15)

Limited‐memory polynomial methods for large‐scale matrix functions ⋮ Rounding error analysis of linear recurrences using generating series ⋮ Computing Derivatives of Jacobi Polynomials Using Bernstein Transformation and Differentiation Matrix ⋮ Algorithms for the integration and derivation of Chebyshev series. ⋮ The three-term recursion for Chebyshev polynomials is mixed forward-backward stable ⋮ Accurate polynomial root-finding methods for symmetric tridiagonal matrix eigenproblems ⋮ Accurate evaluation of a polynomial in Chebyshev form ⋮ 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 ⋮ Accurate evaluation of polynomials in Legendre basis ⋮ \textsf{ORTHOPOLY}: a library for accurate evaluation of series of classical orthogonal polynomials and their derivatives ⋮ Numerical evaluation of the \(p\)th derivative of Jacobi series ⋮ On the numerical evaluation of linear recurrences ⋮ Towards a reliable implementation of least-squares collocation for higher index differential-algebraic equations. I: Basics and ansatz function choices

Uses Software

• mctoolbox

Cites Work

• On algorithms for the summation of certain special functions
• Rounding error propagation in polynomial evaluation schemes
• Generation and Use of Orthogonal Polynomials for Data-Fitting with a Digital Computer
• Using qr-decompositions in the numerical solution of linear recurrence relations
• Error Control with Polynomial Approximations
• Error Analysis for Polynomial Evaluation
• An Error Analysis of the Modified Clenshaw Method for Evaluating Chebyshev and Fourier Series
• The Accuracy of Solutions to Triangular Systems
• An Algorithm for Summing Orthogonal Polynomial Series and their Derivatives with Applications to Curve-Fitting and Interpolation
• Error analysis of an algorithm for summing certain finite series
• An error analysis of Goertzel's (Watt's) method for computing Fourier coefficients
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