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On an iterative procedure for obtaining the Perron root of a positive matrix


Author: Richard Bellman
Journal: Proc. Amer. Math. Soc. 6 (1955), 719-725
MSC: Primary 65.0X
DOI: https://doi.org/10.1090/S0002-9939-1955-0071863-X
MathSciNet review: 0071863
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  • [1] R. Bellman, An introduction to the theory of dynamic programming, RAND Report No. R-245, 1953. MR 0061805 (15:887e)
  • [2] -, A survey of the theory of time-lag, retarded control and hereditary processes, RAND Report No. R-271, 1954.
  • [3] -, Some functional equations in the theory of dynamic programming--I, Trans. Amer. Math. Soc. vol. 80 (1955) pp. 51-71. MR 0074692 (17:632a)
  • [4] -, On a new iterative algorithm for finding the solutions of games and linear programming problems, Symposium on Monte Carlo Methods, University of Florida, March, 1954.
  • [5] R. Bellman and J. LaSalle, Non-zero sum games and stochastic processes, RAND Memorandum No. RM-271, 1949.
  • [6] L. Shapley, Stochastic games, Proc. Nat. Acad. Sci. U.S.A. vol. 39 (1953) pp. 1095-1100. MR 0061807 (15:887g)
  • [7] J. von Neumann, Ergebnisse eines Math. Kolloquiums vol. 8 (1937) pp. 73-78.
  • [8] J. von Neumann and O. Morgenstern, Theory of games and economic behavior, Princeton University Press, 1944. MR 0011937 (6:235k)

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DOI: https://doi.org/10.1090/S0002-9939-1955-0071863-X
Article copyright: © Copyright 1955 American Mathematical Society

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