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Mathematics of Computation

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On the error term of symmetric
Gauss-Lobatto quadrature formulae
for analytic functions

Authors: David Hunter and Geno Nikolov
Journal: Math. Comp. 69 (2000), 269-282
MSC (1991): Primary 41A55; Secondary 65D30, 65D35
Published electronically: March 4, 1999
MathSciNet review: 1642754
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Abstract: Gauss-Lobatto quadrature formulae associated with symmetric weight functions are considered. The kernel of the remainder term for classes of analytic functions is investigated on elliptical contours. Sufficient conditions are found ensuring that the kernel attains its maximal absolute value at the intersection point of the contour with either the real or the imaginary axis. The results obtained here are an analogue of some recent results of T. Schira concerning Gaussian quadratures.

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Additional Information

David Hunter
Affiliation: Department of Computing and Mathematics, University of Bradford, BD7 Bradford, West Yorkshire, United Kingdom

Geno Nikolov
Affiliation: Department of Mathematics, University of Sofia, blvd. James Bourchier 5, 1164 Sofia, Bulgaria

Keywords: Gauss-Lobatto quadrature, remainder term for analytic functions, contour integral representation, kernel function
Received by editor(s): October 14, 1997
Received by editor(s) in revised form: March 26, 1998
Published electronically: March 4, 1999
Additional Notes: The second author did this work while he was on leave from the Department of Mathematics, University of Sofia, blvd J. Bourchier 5, 1164 Sofia, Bulgaria. He was supported by a grant from the Royal Society, and by the Bulgarian Ministry of Science, Education and Technologies under Grant MM-513/95
Article copyright: © Copyright 1999 American Mathematical Society