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On the method for numerical integration of Clenshaw and Curtis

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Abstract

Letf(x) be a function, defined and “well behaved” on the finite intervala≦x≦b Clenshaw andCurtis [1] have given a method for the numerical integration off(x) froma tob, based on the approximation off(x) with a finite series of Chebyshev polynomials. We show that this method is asymptotically equivalent to using the trapezoïdal rule for integratingg(y)=f(cosy).

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References

  1. Clenshaw, C. W., andA. R. Curtis: A method for numerical integration on an automatic computer. Numer. Math.2, 197–205 (1960).

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  2. Stegun, Irene A., andM. Abramowitz: Pitfalls in computations. J. soc. Indust. appl. Math.4, 207–219 (1956).

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  3. Imhof, J. P.: Computing the distribution of quadratic forms in normal variables. Biometrika48, 419–426 (1961).

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Authors and Affiliations

  1. The Observatory, Geneva, Switzerland

    J. P. Imhof

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  1. J. P. Imhof
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Imhof, J.P. On the method for numerical integration of Clenshaw and Curtis. Numer. Math. 5, 138–141 (1963). https://doi.org/10.1007/BF01385885

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  • DOI: https://doi.org/10.1007/BF01385885

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