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Title: THE EVALUATION OF DEFINITE INTEGRALS, AND A QUASI-MONTE-CARLO METHOD BASED ON THE PROPERTIES OF ALGEBRAIC NUMBERS

THE EVALUATION OF DEFINITE INTEGRALS, AND A QUASI-MONTE-CARLO METHOD BASED ON THE PROPERTIES OF ALGEBRAIC NUMBERS 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)
Authors:
Publication Date:
OSTI Identifier:4405295
Report Number(s):LA-1342
Resource Type:Technical Report
Data Type:
Resource Relation:Other Information: Orig. Receipt Date: 31-DEC-52
Research Org:Los Alamos Scientific Lab.
Sponsoring Org:USDOE
Country of Publication:United States
Language:English
Subject: PHYSICS; DIFFERENTIAL EQUATIONS; INTEGRALS; MONTE CARLO METHOD