Mathematics of Computation

Author(s): Piotr Gajda; Youming Li; Leszek Plaskota; Grzegorz W. Wasilkowski.
Journal: Math. Comp. 73 (2004), 813-825.
MSC (2000): Primary 65D30, 65C05
Posted: August 19, 2003
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Abstract: We present and analyze a new randomized algorithm for numerical computation of weighted integrals over the unbounded domain $\mathbb{R} ^d$ . The algorithm and its desirable theoretical properties are derived based on certain stochastic assumptions about the integrands. It is easy to implement, enjoys $O(n^{-1/2})$ convergence rate, and uses only standard random number generators. Numerical results are also included.

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Piotr Gajda
Affiliation: Department of Mathematics, Informatics, and Mechanics, Warsaw University, ul. Banacha 2, 02-097 Warsaw, Poland
Email: piotrg@mimuw.edu.pl

Youming Li
Affiliation: Mathematics and Computer Science Department, Georgia Southern University, 0203 Georgia Avenue, Statesboro, Georgia 30460-8093
Email: yming@gasou.edu

Leszek Plaskota
Affiliation: Department of Mathematics, Informatics, and Mechanics, Warsaw University, ul. Banacha 2, 02-097 Warsaw, Poland
Email: leszekp@mimuw.edu.pl

Grzegorz W. Wasilkowski
Affiliation: Department of Computer Science, University of Kentucky, 773 Anderson Hall, Lexington, Kentucky 40506-0046
Email: greg@cs.uky.edu

DOI: 10.1090/S0025-5718-03-01564-3
PII: S 0025-5718(03)01564-3
Keywords: Numerical multiple integration, Monte Carlo methods, average case error
Received by editor(s): February 18, 2002
Received by editor(s) in revised form: July 23, 2002
Posted: August 19, 2003
Copyright of article: Copyright 2003, American Mathematical Society

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