The three-term recursion for Chebyshev polynomials is mixed forward-backward stable

DOI10.1007/s11075-014-9925-xzbMath1326.65031arXiv1312.5677OpenAlexW1994629846WikidataQ59408544 ScholiaQ59408544MaRDI QIDQ494669

Alicja Smoktunowicz, Agata Smoktunowicz, Ewa Pawelec

Publication date: 1 September 2015

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.5677

zbMATH Keywords

Chebyshev polynomialserror analysisroots of polynomialsfloating point arithmeticthree-term recurrence relationmixed forward-backward stability

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Roundoff error (65G50) Computation of special functions and constants, construction of tables (65D20) Numerical computation of roots of polynomial equations (65H04) Numerical aspects of recurrence relations (65Q30)

Related Items (2)

Evaluation of Chebyshev polynomials by a three-term recurrence in floating-point arithmetic ⋮ Faster stochastic trace estimation with a Chebyshev product identity

Uses Software

• mctoolbox
• Chebfun
• OPQ

Cites Work

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• On algorithms for the summation of certain special functions
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• Analysis of a nonlinear system with random characteristics
• A General Condition Number for Polynomials
• Barycentric Lagrange Interpolation
• Error analysis of an algorithm for summing certain finite series
• An error analysis of Goertzel's (Watt's) method for computing Fourier coefficients
• Stability of parallel algorithms to evaluate Chebyshev series
• Rounding error bounds for the Clenshaw and Forsythe algorithms for the evaluation of orthogonal polynomial series

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