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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

Quadrature methods based on complex function values


Author: J. N. Lyness
Journal: Math. Comp. 23 (1969), 601-619
MSC: Primary 65.55
DOI: https://doi.org/10.1090/S0025-5718-1969-0247771-6
MathSciNet review: 0247771
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Abstract: A method of numerical quadrature over a finite interval is described. This method is applicable if the integrand is an analytic function, regular within the circle in the complex plane having the integration interval as diameter. The method is iterative in nature and relies on function values at equally spaced points on this circle. It is flexible enough to take into account certain simple nonanalytic singularities in the integrand lying on the interval of integration or its extension.

Numerical examples are given which illustrate various advantages and disadvantages of this method when compared with standard quadrature procedures.


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DOI: https://doi.org/10.1090/S0025-5718-1969-0247771-6
Article copyright: © Copyright 1969 American Mathematical Society