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On a successive transformation of probability distribution and its application to the analysis of the optimum gradient method

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References

  1. Akaike, H. “On a computation method for eigenvalue problems and its application to statistical analysis,”Annals of the Institute of Statistical Mathematics 10, 1–20 (1958).

    Article  MathSciNet  Google Scholar 

  2. Chernoff, H. and Divinsky, N. “The computation of maximum-likelihood estimates of linear structural equations,” Chapter 10 inStudies in Ecnometric Method, Cowles Commission Monograph 14, Wm. C. Hood and T. C. Koopmans editors, John Wiley and Sons, Inc. New York, (1953).

    Google Scholar 

  3. Crockett, J. B. and Chernoff, H. “Gradient methods of maximization,”Pacific J. Math., 5, 33–50 (1955).

    Article  MathSciNet  Google Scholar 

  4. Forsythe, G. E. “Solving linear algebraic equations can be interesting,”Bull. Amer. Math. Soc., 59, 299–329 (1953).

    Article  MathSciNet  Google Scholar 

  5. Forsythe, A. I. and Forsythe, G. E. “Punched-card experiments with accelerated gradient methods for linear eqations,”Contributions to the Solution of systems of Linear Equations and the Determination of Eigenvalues, N.B.S. Applied Mathematics Series 39, Olga Taussky editor, 55–69 (1954).

  6. Forsythe, G. E. and Motzkin, T. S. “Asymptotic properties of the optimum gradient method,”Bul. Am. Math. Soc., 57, 183 (1951) (Abstract).

    Google Scholar 

  7. Forsythe, G. E. and Motzkin, T. S. “Acceleration of the optimum gradient method,” Preliminary report,Bul. Am. Math. Soc., 57, 304–305 (1951) (Abstract).

    Google Scholar 

  8. Kantrovich, L. V. “Functional analysis and applied mathematics,”Uspekhi Mathematicheskikh Nauk (NS), 3, No. 6, 89–185 (1951).

    MathSciNet  Google Scholar 

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  1. The Institute of Statistical Mathematics, Japan

    Hirotugu Akaike

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  1. Hirotugu Akaike
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Akaike, H. On a successive transformation of probability distribution and its application to the analysis of the optimum gradient method. Ann Inst Stat Math 11, 1–16 (1959). https://doi.org/10.1007/BF01831719

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  • DOI: https://doi.org/10.1007/BF01831719

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