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On the RAS-algorithm

Zum RAS-Algorithmus

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Abstract

Given a nonnegative real (m, n) matrixA and positive vectorsu, v, then the biproportional constrained matrix problem is to find a nonnegative (m, n) matrixB such thatB=diag (x) A diag (y) holds for some vectorsx ∈ ℝm andy ∈ ℝn and the row (column) sums ofB equalu i (v j )i=1,...,m(j=1,..., n). A solution procedure (called the RAS-method) was proposed by Bacharach [1] to solve this problem. The main disadvantage of this algorithm is, that round-off errors slow down the convergence. Here we present a modified RAS-method which together with several other improvements overcomes this disadvantage.

Zusammenfassung

SeiA eine reelle (m, n) Matrix undu, v positive Vektoren. Das nichtnegative Matrixproblem besteht nun in der Aufgabe, eine nichtnegative (m, n) Matrix zu bestimmen, so daßB=diag(x) A diag (y) für Vektorenx ∈ ℝm undy ∈ ℝn gilt undu i (v j )i=1, ...,m (j=1,...,n) die Zeilen- und Spaltensummen vonB darstellen. Eine Lösungsmethode (RAS-Verfahren) wurde von Bacharach [1] vorgeschlagen. Ein wesentlicher Nachteil dieses Algorithmus ist die Verlangsamung der Konvergenzgeschwindigkeit durch Rundungsfehler. Hier schlagen wir einen modifizierten RAS-Algorithmus vor, der zusammen mit anderen Verbesserungen diesen Nachteil überwindet.

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References

  1. Bacharach, M.: Biproportional matrices and input-output change. Cambridge: Cambridge University Press 1970.

    Google Scholar 

  2. Bachem, A., Korte, B.: Estimating input-output matrices. Report No. 7784-OR, Institut für Ökonometrie und Operations Research, Universität Bonn, 1977.

  3. Bachem, A., Korte, B.: Minimum norm problems over transportation problems. Report 79130-OR, Institut für Ökonometrie und Operations Research, Universität Bonn, 1979.

  4. Bingen, F.: Simplification de la démonstration d'un théoréme de M. W. M. Gorman. Note, Université Libre de Bruxelles, Bruxelles, 1965.

    Google Scholar 

  5. Deming, W. E., Stephan, F. F.: On a least-squares adjustment of a sampled frequency table when the expected marginal totals are known. Annals of Mathematical Statistics11, 427–444 (1940).

    Google Scholar 

  6. Fréchet, M.: Sur les tableaux dont les marges et des bornes sont données. Review of the International Statistical Institute28, 10–32 (1960).

    Google Scholar 

  7. Friedlander, D.: A technique for estimating a contigency table, given the marginal total and some supplementary data. Journal of the Royal Statistical SocietyA 124, 412–420 (1961).

    Google Scholar 

  8. Gorman, W. M.: Estimating trends in Leontief matrices, a note on Mr. Bacharach's paper. Note, Nuffield College, Oxford, 1963.

    Google Scholar 

  9. Stone, R.: Input-output and national accounts. Organisation for Economic Co-Operation and Development (OECD), Paris, 1961.

    Google Scholar 

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Authors and Affiliations

  1. Institut für Ökonometrie und Operations Research, Rheinische Friedrich-Wilhelms-Universität Bonn, D-5300, Bonn, Federal Republic of Germany

    A. Bachem & B. Korte

Authors
  1. A. Bachem
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  2. B. Korte
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Additional information

Supported by Sonderforschungsbereich 21 (DFG), Institut für Ökonometrie und Operations Research, Universität Bonn.

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Bachem, A., Korte, B. On the RAS-algorithm. Computing 23, 189–198 (1979). https://doi.org/10.1007/BF02252097

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  • DOI: https://doi.org/10.1007/BF02252097

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