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Matrix analysis of interregional population growth and distribution

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References

  1. Bernardelli, H., “Population Waves,”Journal of the Burma Research Society, XXXI (1941), pp. 1–18.

    Google Scholar 

  2. Brauer, Alfred, “A New Proof of Theorems of Perron and Frobenius on Non-negative Matrices,”Duke Mathematical Journal, XXIV (1957), pp. 367–378.

    Article  Google Scholar 

  3. Debreu, Gerard, and I. N. Herstein, “Non-negative Square Matrices,”Econometrica, XXI (1953), pp. 597–607.

    Google Scholar 

  4. Fisher, Franklin M., “An Alternate Proof and Extension of Solow's Theorem on Non-Negative Square Matrices,”Econometrica, XXX (1962), pp. 349–350.

    Google Scholar 

  5. Frazer, R. A., W. J. Duncan, and A. R. Collar,Elementary Matrices (Cambridge, England: The University Press, 1963).

    Google Scholar 

  6. Gantmacher, F. R.,Matrix Theory, Vol. II, Chapter XIII, “Matrices with Non-negative Elements” (New York: Chelsea Publishing Co., 1959), pp. 50–112.

    Google Scholar 

  7. Goodman, Leo A., “A Further Note on ‘Finite Markov Processes in Psychology’”,Psychometrika, XVIII (1953), pp. 245–248.

    Google Scholar 

  8. Kao, Richard C. W., “Note on Miller's ‘Finite Markov Processes in Psychology’”,Psychometrika, XVIII (1953), pp. 241–243.

    Google Scholar 

  9. Keyfitz, Nathan, “Matrix Multiplication as a Technique of Population Analysis,”Milbank Memorial Fund Quarterly (1964), pp. 68–83.

  10. , “The Population Projection as a Matrix Operator,”Demography, I (1964), pp. 56–73.

    Google Scholar 

  11. Keyfitz, Nathan, “The Intrinsic Rate of Natural Increase and the Dominant Root of the Projection Matrix,”Population Studies (1965), pp. 293–308.

  12. Lee, T. C., G. G. Judge, and T. Takayama, “On Estimating the Transition Probabilities of a Markov Process,”Journal of Farm Economics, (1965), pp. 742–762.

  13. Leslie, P. H., “On the Use of Matrices in Certain Population Mathematics,”Biometrika, XXXIII (1945), pp. 183–212

    Google Scholar 

  14. Lopez, Alvaro,Problems in Stable Population Theory (Princeton, N. J.: Office of Population Research, Princeton University, 1961).

    Google Scholar 

  15. Madansky, Albert, “Least Squares Estimation in Finite Markov Processes,”Psychometrika, XXIV (1959), pp. 137–144.

    Google Scholar 

  16. Miller, George A., “Finite Markov Processes in Psychology,”Psychometrika, XVII (1952), pp. 149–167.

    Google Scholar 

  17. Rogers, Andrei, “A Markovian Policy Model of Interregional Migration,”Papers and Proceedings of the Regional Science Association, XVII (1966).

  18. Rogers, Andrei,Projected Population Growth in California Regions: 1960–1980, (Center for Planning and Development Research, University of California, December 1965).

  19. —, “Matrix Methods of Population Analysis,”Journal of the American Institute of Planners, XXXII (January 1966), pp. 40–44.

    Google Scholar 

  20. Rogers, Andrei, “Sensitivity Tests of a Model of Population Growth in California Regions,”Proceedings of the Regional Science Association, (Western Section Papers, Santa Barbara, January 1966), forthcoming.

  21. Rogers, Andrei, “A Regression Analysis of Interregional Migration in California,”The Review of Economics and Statistics, forthcoming.

  22. Rogers, Andrei, “Experiments with a Matrix Model of Population Growth and Distribution,”Proceedings of the Fourth International Conference on Operations Research, (Cambridge, August 1966), forthcoming.

  23. —, “The Dominant characteristic Root, Its characteristic Vector, and the Stable Interregional Population Distribution,” preprint, (Center for Planning and Development Research, Uversity of California, Berkeley, February 1966).

    Google Scholar 

  24. —, “A Note on the Temporal Decomposition of Interpoint Transition Matrices,”Journal of Regional Science, VI:2 (Fall 1966), forthcoming.

    Google Scholar 

  25. —, “The Multiregional Matrix Growth Operator and the Stable Interregional Age Structure,”Demography, III:2 (Fall 1966).

    Google Scholar 

  26. Rogers, Andrei, and Robert Miller, “Estimating a Matrix Population Growth Operator from Distributional Time Series,”Annals of the Association of American Geographers forthcoming.

  27. Samuelson, H., “On the Perron-Frobenius Theorem,”Michigan Mathematical Journal, IV (1957), pp. 189–193.

    Google Scholar 

  28. Solow, Robert M., “On the Structure of Linear Models,”Econometrica, XX (1952), pp. 29–46.

    Google Scholar 

  29. Telser, Lester G., “Least Squares Estimates of Transition Probabilities,” inMeasurement in Economics, F. Christ (ed.), (Palo Alto, California: Stanford University Press, 1963), pp. 272–92.

    Google Scholar 

  30. Theil, Henry and Guido Rey, “A Quadratic Programming Approach to the Estimation of Transition Probabilities,” Report No. 6426, (International Center for Management Science, Rotterdam, Holland, November 1964), mimeo, 10 p.

    Google Scholar 

  31. Woodbury, Max A., “Characteristic Roots of Input-Output Matrices,” inEconomic Activity Analysis, O. Morgenstern (ed.), (New York: John Wiley & Sons, 1954), pp. 365–382.

    Google Scholar 

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Authors
  1. Andrei Rogers
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The author is associated with the University of California, Berkeley, U.S.A.

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Rogers, A. Matrix analysis of interregional population growth and distribution. Papers of the Regional Science Association 18, 177–196 (1967). https://doi.org/10.1007/BF01940322

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