THE EVALUATION OF DEFINITE INTEGRALS, AND A QUASI-MONTE-CARLO METHOD BASED ON THE PROPERTIES OF ALGEBRAIC NUMBERS
Description/Abstract
A formula is given for the approximate evaluation of multiple definite integrals using the ergodic property of a certain transformation of the unit cube into itself. Estimates of the rate of convergence are made for sufficiently smooth integrand. The work was motivated by a belief, that appeared at one time justified, that a substantial improvement of the accuracy of Monte Carlo method would result from use of the principles described herein. Although that belief proved groundless in numerical tests, it is deemed worthwhile to give this report of the work. Part of the theoretical development, the work of L.G. Peck, will be reported independently. (auth)
| DOI | 10.2172/4405295 |
|---|---|
| Creator/Author: | Richtmyer, R.D. |
| Publication Date: | 1951 Oct 13 |
| OSTI Identifier: | OSTI ID: 4405295 |
| Report Number(s): | LA-1342 |
| DOI: | 10.2172/4405295 |
| Resource Type: | Technical Report |
| Resource Relation: | Other Information: Orig. Receipt Date: 31-DEC-52 |
| Research Org: | Los Alamos Scientific Lab. |
| Sponsoring Org: | USDOE |
| Subject: | PHYSICS; DIFFERENTIAL EQUATIONS; INTEGRALS; MONTE CARLO METHOD |
| Country of Publication: | United States |
| Language: | English |
| Format: | Size: Pages: 30 |
| Update Date: | 2008 Feb 05 |
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