Matrix inversion by a Monte Carlo method
Author:
Publisher
American Mathematical Society (AMS)
Subject
Applied Mathematics,Computational Mathematics,Algebra and Number Theory
Link
http://www.ams.org/mcom/1950-04-031/S0025-5718-1950-0038138-X/S0025-5718-1950-0038138-X.pdf
Reference2 articles.
1. A. Kolmogoroff, Grundbegriffe der Wahrscheinlichkeitsrechnung, New York, 1946, p. 59. The writers are indebted to T. E. Harris for this reference.
2. The fact that 𝜎ᵢⱼ=∞ 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 𝜎ᵢⱼ=∞, the accumulated payment after 𝑁 games cannot be normed so as to be asymptotically normally distributed as 𝑁→∞. 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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