Improved Monte Carlo method for evaluating multidimensional integrals. [In Algol, PL-I, or FORTRAN for IBM 360/75 (FORTRAN listing included)]
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)
- Research Organization:
- Univ. of Illinois at Urbana-Champaign, IL (United States)
- DOE Contract Number:
- EY-76-S-02-2218
- OSTI ID:
- 7218290
- Report Number(s):
- COO-2218-79
- Resource Relation:
- Other Information: Thesis
- Country of Publication:
- United States
- Language:
- English
Similar Records
FBSAM data transmission package for IBM 360/370 computers. [For rapid movement of large blocks of data directly between user storage arrays and magnetic disk data sets, in FORTRAN IV and assembly language]
Algorithm 530: an algorithm for computing the eigensystem of skew-symmetric matrices and a class of symmetric matrices (F2). [TRIZD, IMZD, TBAKZD, in FORTRAN for IBM, 360/91]