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Mathematics of Computation

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Matrix inversion by a Monte Carlo method


Authors: George E. Forsythe and Richard A. Leibler
Journal: Math. Comp. 4 (1950), 127-129
MSC: Primary 65.0X
DOI: https://doi.org/10.1090/S0025-5718-1950-0038138-X
MathSciNet review: 0038138
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  • [2] A. Kolmogoroff, Grundbegriffe der Wahrscheinlichkeitsrechnung, New York, 1946, p. 59. The writers are indebted to T. E. Harris for this reference.
  • [3] The fact that $ {\sigma _{ij}} = \infty $ does not interfere with the convergence of the average value of $ N$ games to $ {({B^{ - 1}})_{ij}}$. However, conventional error estimates in terms of variances no longer apply and, in at least certain matrix inversions where $ {\sigma _{ij}} = \infty $, the accumulated payment after $ N$ games cannot be normed so as to be asymptotically normally distributed as $ N \to \infty $. See W. Feller, ``Über den zentralen Grenzwertsatz der Wahrscheinlichkeitsrechnung,'' Mathematische Zeitschrift, v. 40, 1935, p. 521-559 and v. 42, 1937, p. 301-312, and ``Über das Gesetz der grossen Zahlen,'' Szeged, Acta Univ., Acta Scient. Math., v. 8, 1937, p. 191-201.

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DOI: https://doi.org/10.1090/S0025-5718-1950-0038138-X
Article copyright: © Copyright 1950 American Mathematical Society