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Mathematics of Computation

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Asymptotic estimation of Gaussian quadrature error for a nonsingular integral in potential theory

Author: David M. Hough
Journal: Math. Comp. 71 (2002), 717-727
MSC (2000): Primary 41A55; Secondary 31C20
Published electronically: November 21, 2001
MathSciNet review: 1885623
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Abstract: This paper considers the $n$-point Gauss-Jacobi approximation of nonsingular integrals of the form $\int_{-1}^1 \mu(t) \phi(t) \log (z-t)\, {d}t$, with Jacobi weight $\mu$ and polynomial $\phi$, and derives an estimate for the quadrature error that is asymptotic as $n \to \infty$. The approach follows that previously described by Donaldson and Elliott. A numerical example illustrating the accuracy of the asymptotic estimate is presented. The extension of the theory to similar integrals defined on more general analytic arcs is outlined.

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Additional Information

David M. Hough
Affiliation: MIS-Maths, Coventry University, Coventry CV1 5FB, United Kingdom

Received by editor(s): October 13, 1999
Received by editor(s) in revised form: July 14, 2000
Published electronically: November 21, 2001
Article copyright: © Copyright 2001 American Mathematical Society