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General principles of antithetic variates

Published online by Cambridge University Press:  24 October 2008

J. M. Hammersley  and
J. G. Mauldon
J. M. Hammersley
Affiliation:
Trinity CollegeOxford
J. G. Mauldon
Affiliation:
Corpus Christi CollegeOxford
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Extract

1. In (2) the idea of antithetic variates in Monte Carlo work is introduced and applied to the estimation of integrals. The present paper studies the general theoretical structure of antithetic variates. We have made only limited progress and present various unsolved problems as a challenge to the reader.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 52 , Issue 3 , July 1956 , pp. 476 - 481
Copyright
Copyright © Cambridge Philosophical Society 1956

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References

REFERENCES

(1)Birkhoff, G.Three observations on linear algebra. Rev. Univ. Tucumán, A, 5 (1946), 147–51 (Spanish).Google Scholar
(2)Hammersley, J. M. and Morton, K. W.A new Monte Carlo technique: antithetic variates. Proc. Camb. phil. Soc. 52 (1956), 449–75.CrossRefGoogle Scholar
(3)Horn, A.Doubly stochastic matrices and the diagonal of a rotation matrix. Amer. J. Math. 76 (1954), 620–30.CrossRefGoogle Scholar