On the convergence of Hunter's quadrature rule for Cauchy principal value integrals |
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Authors: | David Elliott |
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Institution: | (1) Department of Mathematics, University of Tasmania, 7001 Hobart, Tasmania, Australia |
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Abstract: | Hunter's (n+1)-point quadrature rule for the approximate evaluation of the Cauchy principal value integralf
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–1 (w(x)f(x)/(x – ))dx, –1< <1, is based on approximatingf by the polynomial which interpolatesf at the point and then zeros of the orthogonal polynomialp
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generated by the weight functionw. Sufficient conditions are given to ensure the convergence of a suitably chosen subsequence of the quadrature rules to the integral, whenf is Hölder continuous on –1,1]. |
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