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Theoretical Properties of Biproportional Matrix Adjustments

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  • S M Macgill

    (School of Geography, University of Leeds, Leeds LS2 9JT, England)

Abstract

The basic uniqueness and existence properties of biproportional matrix solutions are reviewed and a direct and constructive proof of the convergence of an iterative routine commonly adopted to adjust a given nonnegative matrix to produce a second matrix (biproportional to the first), whose row and column sums are given strictly positive numbers, is offered. Existing convergence proofs, most of which are limited to particular cases of the present form, are considered.

Suggested Citation

  • S M Macgill, 1977. "Theoretical Properties of Biproportional Matrix Adjustments," Environment and Planning A, , vol. 9(6), pages 687-701, June.
    • Handle: RePEc:sae:envira:v:9:y:1977:i:6:p:687-701
    DOI: 10.1068/a090687
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    Cited by:

    1. Lan, Jun & Malik, Arunima & Lenzen, Manfred & McBain, Darian & Kanemoto, Keiichiro, 2016. "A structural decomposition analysis of global energy footprints," Applied Energy, Elsevier, vol. 163(C), pages 436-451.
    2. R. S. Thilakaratne & S. C. Wirasinghe, 2016. "Implementation of Bus Rapid Transit (BRT) on an optimal segment of a long regular bus route," International Journal of Urban Sciences, Taylor & Francis Journals, vol. 20(1), pages 15-29, March.
    3. Erik Dietzenbacher & Bart Los, 2000. "Structural Decomposition Analyses with Dependent Determinants," Economic Systems Research, Taylor & Francis Journals, vol. 12(4), pages 497-514.
    4. Andre Lemelin, 2009. "A Gras Variant Solving For Minimum Information Loss," Economic Systems Research, Taylor & Francis Journals, vol. 21(4), pages 399-408.
    5. Casiano A. Manrique-de-Lara-Peñate & Dolores R. Santos-Peñate, 2017. "SAM updating using multi-objective optimization techniques," Papers in Regional Science, Wiley Blackwell, vol. 96(3), pages 647-667, August.
    6. Roberto Mínguez & Jan Oosterhaven & Fernando Escobedo, 2009. "Cell‐Corrected Ras Method (Cras) For Updating Or Regionalizing An Input–Output Matrix," Journal of Regional Science, Wiley Blackwell, vol. 49(2), pages 329-348, May.
    7. Friedrich Pukelsheim, 2014. "Biproportional scaling of matrices and the iterative proportional fitting procedure," Annals of Operations Research, Springer, vol. 215(1), pages 269-283, April.

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