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Title: Improved Monte Carlo method for evaluating multidimensional integrals. [In Algol, PL-I, or FORTRAN for IBM 360/75 (FORTRAN listing included)]

Abstract

The goal of this work was to develop an improved Monte Carlo method and implement a computer code for performing automatic integration of multidimensional integrals of the form ..integral..f(X)dX over a closed region in k-dimensional Euclidean space, where X is a point in the space and DX = dx/sub 1/dx/sub 2/...dx/sub k/. The scheme is ''automatic'' in the sense that it returns a value for the integral when the user inserts the limits of the integral, a function subroutine for computing f(X), and a tolerance. A survey on currently known methods of multiple integration is given first, and the MCSS scheme of Halton and Zeidman is found to be the best one implemented as a computer program. Improvements were made to make the sequential stratification technique more powerful and efficient. The resulting MCSSAV algorithm is readily programable in Algol and PL/I. Because of its recursive feature, programing it in FORTRAN is less straightforward; a flowchart and listing are given for this language. For lower-dimensional integrals, the program achieves accuracies of 4 to 5 significant figures for small amounts of CPU time, e.g., 30 seconds on an IBM 360/75. Test results for higher-dimensional integrals are not very satisfactory due to themore » biased distribution of random samples in n-space simulated by the Lehmer pseudorandom number generator. Several related subroutines for sampling and making estimates are also listed. 6 figures, 2 tables. (RWR)« less

Authors:
Publication Date:
Research Org.:
Univ. of Illinois at Urbana-Champaign, IL (United States)
OSTI Identifier:
7218290
Report Number(s):
COO-2218-79
DOE Contract Number:  
EY-76-S-02-2218
Resource Type:
Technical Report
Resource Relation:
Other Information: Thesis
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; COMPUTER CODES; M CODES; INTEGRALS; EVALUATION; ALGOL; FORTRAN; IBM COMPUTERS; MONTE CARLO METHOD; PL-1 LANGUAGE; COMPUTERS; MATHEMATICAL LOGIC; PROGRAMMING LANGUAGES; 990200* - Mathematics & Computers

Citation Formats

Yuen, S K. Improved Monte Carlo method for evaluating multidimensional integrals. [In Algol, PL-I, or FORTRAN for IBM 360/75 (FORTRAN listing included)]. United States: N. p., 1977. Web. doi:10.2172/7218290.
Yuen, S K. Improved Monte Carlo method for evaluating multidimensional integrals. [In Algol, PL-I, or FORTRAN for IBM 360/75 (FORTRAN listing included)]. United States. https://doi.org/10.2172/7218290
Yuen, S K. 1977. "Improved Monte Carlo method for evaluating multidimensional integrals. [In Algol, PL-I, or FORTRAN for IBM 360/75 (FORTRAN listing included)]". United States. https://doi.org/10.2172/7218290. https://www.osti.gov/servlets/purl/7218290.
@article{osti_7218290,
title = {Improved Monte Carlo method for evaluating multidimensional integrals. [In Algol, PL-I, or FORTRAN for IBM 360/75 (FORTRAN listing included)]},
author = {Yuen, S K},
abstractNote = {The goal of this work was to develop an improved Monte Carlo method and implement a computer code for performing automatic integration of multidimensional integrals of the form ..integral..f(X)dX over a closed region in k-dimensional Euclidean space, where X is a point in the space and DX = dx/sub 1/dx/sub 2/...dx/sub k/. The scheme is ''automatic'' in the sense that it returns a value for the integral when the user inserts the limits of the integral, a function subroutine for computing f(X), and a tolerance. A survey on currently known methods of multiple integration is given first, and the MCSS scheme of Halton and Zeidman is found to be the best one implemented as a computer program. Improvements were made to make the sequential stratification technique more powerful and efficient. The resulting MCSSAV algorithm is readily programable in Algol and PL/I. Because of its recursive feature, programing it in FORTRAN is less straightforward; a flowchart and listing are given for this language. For lower-dimensional integrals, the program achieves accuracies of 4 to 5 significant figures for small amounts of CPU time, e.g., 30 seconds on an IBM 360/75. Test results for higher-dimensional integrals are not very satisfactory due to the biased distribution of random samples in n-space simulated by the Lehmer pseudorandom number generator. Several related subroutines for sampling and making estimates are also listed. 6 figures, 2 tables. (RWR)},
doi = {10.2172/7218290},
url = {https://www.osti.gov/biblio/7218290}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Sat Jan 01 00:00:00 EST 1977},
month = {Sat Jan 01 00:00:00 EST 1977}
}