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A Comparative Study of Algorithms for Matrix Balancing


  • Michael H. Schneider

    (Johns Hopkins University, Baltimore, Maryland)

  • Stavros A. Zenios

    (University of Pennsylvania, Philadelphia, Pennsylvania)


The problem of adjusting the entries of a large matrix to satisfy prior consistency requirements occurs in economics, urban planning, statistics, demography, and stochastic modeling; these problems are called Matrix Balancing Problems . We describe five applications of matrix balancing and compare the algorithmic and computational performance of balancing procedures that represent the two primary approaches for matrix balancing—matrix scaling and nonlinear optimization. The algorithms we study are the RAS algorithm, a diagonal similarity scaling algorithm, and a truncated Newton algorithm for network optimization. We present results from computational experiments with large-scale problems based on producing consistent estimates of Social Accounting Matrices for developing countries.

Suggested Citation

  • Michael H. Schneider & Stavros A. Zenios, 1990. "A Comparative Study of Algorithms for Matrix Balancing," Operations Research, INFORMS, vol. 38(3), pages 439-455, June.
  • Handle: RePEc:inm:oropre:v:38:y:1990:i:3:p:439-455
    DOI: 10.1287/opre.38.3.439

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    Cited by:

    1. Burfisher, Mary & Thierfelder, Karen & Hanson, Kenneth, 1992. "Data Base for a Computable General Equilibrium Model of the Agricultural Sectors of the United States and Mexico and Their Interactions," Staff Reports 278680, United States Department of Agriculture, Economic Research Service.
    2. Andrea Consiglio & Michele Tumminello & Stavros A. Zenios, 2018. "Pricing Sovereign Contingent Convertible Debt," Journal of Enterprising Culture (JEC), World Scientific Publishing Co. Pte. Ltd., vol. 21(08), pages 1-36, December.
    3. Peter Stephensen, 2012. "SBAM: An Algorithm for Pair Matching," DREAM Working Paper Series 201201, Danish Rational Economic Agents Model, DREAM.
    4. Steven Diamond & Stephen Boyd, 2017. "Stochastic Matrix-Free Equilibration," Journal of Optimization Theory and Applications, Springer, vol. 172(2), pages 436-454, February.
    5. Coleman, Charles, 2016. "A SAS® Macro for the Generalized RAS Algorithm," MPRA Paper 77651, University Library of Munich, Germany, revised 19 Mar 2017.
    6. Fahimeh Biglari & Farideh Mahmoodpur, 2016. "Scaling Damped Limited-Memory Updates for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 177-188, July.
    7. Jose Fique, 2017. "Retrieving Implied Financial Networks from Bank Balance-Sheet and Market Data," Staff Working Papers 17-30, Bank of Canada.
    8. Firano, Zakaria & Filali adib, Fatine, 2019. "Intersectorial contagion risk in Morocco," MPRA Paper 95343, University Library of Munich, Germany.
    9. Patrizio Lecca & Javier Barbero Jimenez & Martin Aaroe Christensen & Andrea Conte & Francesco Di Comite & Jorge Diaz-Lanchas & Olga Diukanova & Giovanni Mandras & Damiaan Persyn & Stylianos Sakkas, 2018. "RHOMOLO V3:A Spatial Modelling Framework," JRC Working Papers JRC111861, Joint Research Centre (Seville site).
    10. Dale T. Manning & J. Edward Taylor & James E. Wilen, 2018. "General Equilibrium Tragedy of the Commons," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 69(1), pages 75-101, January.
    11. Jeffrey C. Peters & Thomas W. Hertel, 2016. "Matrix balancing with unknown total costs: preserving economic relationships in the electric power sector," Economic Systems Research, Taylor & Francis Journals, vol. 28(1), pages 1-20, March.
    12. Sohani Liyanage & Hussein Dia & Rusul Abduljabbar & Saeed Asadi Bagloee, 2019. "Flexible Mobility On-Demand: An Environmental Scan," Sustainability, MDPI, Open Access Journal, vol. 11(5), pages 1-39, February.


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