A Monte Carlo algorithm for weighted integration over ℝ d

Piotr Gajda; Youming Li; Leszek Plaskota; Grzegorz W. Wasilkowski

doi:10.1090/S0025-5718-03-01564-3

A Monte Carlo algorithm for weighted integration over ℝ ^d

Piotr Gajda
, Youming Li
, Leszek Plaskota
, Grzegorz W. Wasilkowski

Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

We present and analyze a new randomized algorithm for numerical computation of weighted integrals over the unbounded domain 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.

Original language	English
Pages (from-to)	813-825
Number of pages	13
Journal	Mathematics of Computation
Volume	73
Issue number	246
DOIs	https://doi.org/10.1090/S0025-5718-03-01564-3
State	Published - Apr 2004

Keywords

Average case error
Monte Carlo methods
Numerical multiple integration

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

Access to Document

10.1090/S0025-5718-03-01564-3

Cite this

@article{9bbf0f13d07f494b8454ad73ca554b06,

title = "A Monte Carlo algorithm for weighted integration over ℝ d ",

abstract = "We present and analyze a new randomized algorithm for numerical computation of weighted integrals over the unbounded domain 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.",

keywords = "Average case error, Monte Carlo methods, Numerical multiple integration",

author = "Piotr Gajda and Youming Li and Leszek Plaskota and Wasilkowski, \{Grzegorz W.\}",

year = "2004",

month = apr,

doi = "10.1090/S0025-5718-03-01564-3",

language = "English",

volume = "73",

pages = "813--825",

number = "246",

}

TY - JOUR

T1 - A Monte Carlo algorithm for weighted integration over ℝ d

AU - Gajda, Piotr

AU - Li, Youming

AU - Plaskota, Leszek

AU - Wasilkowski, Grzegorz W.

PY - 2004/4

Y1 - 2004/4

N2 - We present and analyze a new randomized algorithm for numerical computation of weighted integrals over the unbounded domain 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.

AB - We present and analyze a new randomized algorithm for numerical computation of weighted integrals over the unbounded domain 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.

KW - Average case error

KW - Monte Carlo methods

KW - Numerical multiple integration

UR - https://www.scopus.com/pages/publications/1642602849

UR - https://www.scopus.com/pages/publications/1642602849#tab=citedBy

U2 - 10.1090/S0025-5718-03-01564-3

DO - 10.1090/S0025-5718-03-01564-3

M3 - Article

AN - SCOPUS:1642602849

SN - 0025-5718

VL - 73

SP - 813

EP - 825

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 246

ER -