Asymptotic estimation of Gaussian quadrature error for a nonsingular integral in potential theory
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- by David M. Hough PDF
- Math. Comp. 71 (2002), 717-727 Request permission
Abstract:
This paper considers the $n$-point Gauss-Jacobi approximation of nonsingular integrals of the form $\int _{-1}^1 \mu (t) \phi (t) \log (z-t) \mathrm {d}t$, 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.References
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Additional Information
- David M. Hough
- Affiliation: MIS-Maths, Coventry University, Coventry CV1 5FB, United Kingdom
- Email: d.hough@coventry.ac.uk
- Received by editor(s): October 13, 1999
- Received by editor(s) in revised form: July 14, 2000
- Published electronically: November 21, 2001
- © Copyright 2001 American Mathematical Society
- Journal: Math. Comp. 71 (2002), 717-727
- MSC (2000): Primary 41A55; Secondary 31C20
- DOI: https://doi.org/10.1090/S0025-5718-01-01366-7
- MathSciNet review: 1885623