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On the identity of two solution algorithms of the ‘improved normalized squared differences’ matrix adjustment model

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  • Tamas Revesz

    (Corvinus University of Budapest)

Abstract

The paper is a supplement for an article recently published in this journal. That paper proved that if the sign-preservation requirement is dropped then the solution of the so-called improved normalized squared differences (INSD) two-directional matrix adjustment model is the same as the result of the ‘additive correction iteration algorithm’ which the author has been using successfully for decades. It also argued that if the sign-preservation requirement is dropped then the iteration procedure suggested by the authors of the INSD-model boils down to the same algorithm. Since the formal proof of this statement was not available at the time, in this paper the author duly publishes the three-and-a-half pages long proof he elaborated. In the conclusion the merit of this and similar, yet barely rigorously analysed iteration algorithms and the possible useful extensions are also outlined.

Suggested Citation

  • Tamas Revesz, 2025. "On the identity of two solution algorithms of the ‘improved normalized squared differences’ matrix adjustment model," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 33(1), pages 315-332, March.
    • Handle: RePEc:spr:cejnor:v:33:y:2025:i:1:d:10.1007_s10100-024-00924-1
    DOI: 10.1007/s10100-024-00924-1
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    References listed on IDEAS

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    1. Juan Manuel Valderas‐Jaramillo & José Manuel Rueda‐Cantuche, 2021. "The multidimensional nD‐GRAS method: Applications for the projection of multiregional input–output frameworks and valuation matrices," Papers in Regional Science, Wiley Blackwell, vol. 100(6), pages 1599-1624, December.
    2. G. Günlük‐Şenesen & J. M. Bates, 1988. "Some Experiments with Methods of Adjusting Unbalanced Data Matrices," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 151(3), pages 473-490, May.
    3. Umed Temurshoev & Colin Webb & Norihiko Yamano, 2011. "Projection Of Supply And Use Tables: Methods And Their Empirical Assessment," Economic Systems Research, Taylor & Francis Journals, vol. 23(1), pages 91-123.
    4. Manfred Lenzen & Daniel D. Moran & Arne Geschke & Keiichiro Kanemoto, 2014. "A Non-Sign-Preserving Ras Variant," Economic Systems Research, Taylor & Francis Journals, vol. 26(2), pages 197-208, June.
    5. Wenfeng Huang & Shintaro Kobayashi & Hajime Tanji, 2008. "Updating an Input-Output Matrix with Sign-preservation: Some Improved Objective Functions and their Solutions," Economic Systems Research, Taylor & Francis Journals, vol. 20(1), pages 111-123.
    6. Michael Lahr & Louis de Mesnard, 2004. "Biproportional Techniques in Input-Output Analysis: Table Updating and Structural Analysis," Economic Systems Research, Taylor & Francis Journals, vol. 16(2), pages 115-134.
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