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).
Similar content being viewed by others
References
Clenshaw, C. W., andA. R. Curtis: A method for numerical integration on an automatic computer. Numer. Math.2, 197–205 (1960).
Stegun, Irene A., andM. Abramowitz: Pitfalls in computations. J. soc. Indust. appl. Math.4, 207–219 (1956).
Imhof, J. P.: Computing the distribution of quadratic forms in normal variables. Biometrika48, 419–426 (1961).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01385885