Gauss type quadrature rules for Cauchy principal value integrals

Authors:
David Elliott and D. F. Paget

Journal:
Math. Comp. **33** (1979), 301-309

MSC:
Primary 65D32; Secondary 41A55

DOI:
https://doi.org/10.1090/S0025-5718-1979-0514825-2

MathSciNet review:
514825

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Abstract: Two quadrature rules for the approximate evaluation of Cauchy principal value integrals, with nodes at the zeros of appropriate orthogonal polynomials, are discussed. An expression for the truncation error, in terms of higher order derivatives, is given for each rule. In addition, two theorems, containing sufficient conditions for the convergence of the sequence of quadrature rules to the integral, are proved.

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DOI:
https://doi.org/10.1090/S0025-5718-1979-0514825-2

Article copyright:
© Copyright 1979
American Mathematical Society