Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Gaussian quadrature for sums: A rapidly convergent summation scheme

Author: H. Monien
Journal: Math. Comp. 79 (2010), 857-869
MSC (2000): Primary 40A25; Secondary 33C90, 65D32, 33F05
Published electronically: July 21, 2009
MathSciNet review: 2600547
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Gaussian quadrature is a well-known technique for numerical integration. Recently Gaussian quadrature with respect to discrete measures corresponding to finite sums has found some new interest. In this paper we apply these ideas to infinite sums in general and give an explicit construction for the weights and abscissae of Gaussian formulas. The abscissae of the Gaussian summation have a very interesting asymptotic distribution function with a kink singularity. We apply the Gaussian summation technique to two problems which have been discussed in the literature. We find that the Gaussian summation has a very rapid convergence rate for the Hardy-Littlewood sum for a large range of parameters.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 40A25, 33C90, 65D32, 33F05

Retrieve articles in all journals with MSC (2000): 40A25, 33C90, 65D32, 33F05

Additional Information

H. Monien
Affiliation: Bethe Center for Theoretical Physics, Universität Bonn, Nussallee 12, 53115 Bonn, Germany

Received by editor(s): December 19, 2006
Received by editor(s) in revised form: October 16, 2008, and April 3, 2009
Published electronically: July 21, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society