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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References | Similar Articles | Additional Information

**[1]**Richard Bellman,*An introduction to the theory of dynamic programming*, The Rand Corporation, Santa Monica, Calif., 1953. MR**0061805****[2]**-,*A survey of the theory of time-lag, retarded control and hereditary processes*, RAND Report No. R-271, 1954.**[3]**R. Bellman,*Some functional equations in the theory of dynamic programming. I. Functions of points and point transformations*, Trans. Amer. Math. Soc.**80**(1955), 51–71. MR**0074692**, https://doi.org/10.1090/S0002-9947-1955-0074692-0**[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. S. Shapley,*Stochastic games*, Proc. Nat. Acad. Sci. U. S. A.**39**(1953), 1095–1100. MR**0061807****[7]**J. von Neumann, Ergebnisse eines Math. Kolloquiums vol. 8 (1937) pp. 73-78.**[8]**John von Neumann and Oskar Morgenstern,*Theory of Games and Economic Behavior*, Princeton University Press, Princeton, New Jersey, 1944. MR**0011937**

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DOI:
https://doi.org/10.1090/S0002-9939-1955-0071863-X

Article copyright:
© Copyright 1955
American Mathematical Society