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Error Analysis of Clenshaw's Algorithm for Evaluating Derivatives of a Polynomial

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Abstract

A forward rounding error analysis is presented for the extended Clenshaw algorithm due to Skrzipek for evaluating the derivatives of a polynomial expanded in terms of orthogonal polynomials. Reformulating in matrix notation the three-term recurrence relation satisfied by orthogonal polynomials facilitates the estimate of the rounding error for the m-th derivative, which is recursively estimated in terms of the one for the (m − 1)-th derivative. The rounding errors in an important case of Chebyshev polynomial are discussed in some detail.

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Authors and Affiliations

  1. Department of Information Science, Faculty of Engineering, Fukui University, Fukui, 910-8507, Japan

    Takemitsu Hasegawa

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  1. Takemitsu Hasegawa
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Hasegawa, T. Error Analysis of Clenshaw's Algorithm for Evaluating Derivatives of a Polynomial. BIT Numerical Mathematics 41, 1019–1028 (2001). https://doi.org/10.1023/A:1021993312929

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  • DOI: https://doi.org/10.1023/A:1021993312929

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