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Backward stability of Clenshaw's algorithm

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Publication:1864779
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DOI10.1023/A:1022001931526zbMath1019.65004MaRDI QIDQ1864779

Alicja Smoktunowicz

Publication date: 14 May 2003

Published in: BIT (Search for Journal in Brave)


zbMATH Keywords

Chebyshev polynomialsorthogonal polynomialsnumerical stabilityroundoff errorsClenshaw's algorithmseries summation


Mathematics Subject Classification ID

Roundoff error (65G50) Numerical computation of matrix norms, conditioning, scaling (65F35) Numerical summation of series (65B10)


Related Items (9)

A new efficient algorithm for polynomial interpolation ⋮ Limited‐memory polynomial methods for large‐scale matrix functions ⋮ On computing modified moments for half-range Hermite weights ⋮ The three-term recursion for Chebyshev polynomials is mixed forward-backward stable ⋮ Accurate evaluation of a polynomial in Chebyshev form ⋮ On improving the accuracy of Horner's and Goertzel's algorithms ⋮ Stable Computation of Generalized Matrix Functions via Polynomial Interpolation ⋮ Accurate evaluation of polynomials in Legendre basis ⋮ Towards a reliable implementation of least-squares collocation for higher index differential-algebraic equations. I: Basics and ansatz function choices




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