Advertisement

Cybernetics and Systems Analysis

, Volume 50, Issue 3, pp 368–373 | Cite as

Maximum Singular Value of Matrix and its Economic Interpretation

  • P. I. StetsyukEmail author
  • J.-F. Emmenegger
Article
  • 78 Downloads

Abstract

We prove that the maximum singular value of the matrix and the corresponding singular vectors are the optimal solution for a special quadratic optimization problem. We consider the economic interpretation of the optimal solution for the linear model of production and for the productive Leontief model. We relate the optimal solution to the Frobenius number and vectors and compare the Frobenius numbers and maximum singular values for Leontief inverse matrix in the 15-sectoral balance of Ukraine for 2003–2009.

Keywords

maximum singular number quadratic optimization problem Frobenius number and vectors irreducible matrix Leontief inverse matrix 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S. A. Ashmanov, Introduction to Mathematical Economics [in Russian], Nauka, Moscow (1984).Google Scholar
  2. 2.
    O. I. Ponomarenko, M. O. Perestyuk, and V. M. Burym, Modern Economic Analysis. Pt. 2: Macroeconomics [in Russian], Vyshcha Shkola, Kyiv (2004).Google Scholar
  3. 3.
    P. I. Stetsyuk, “The quadratic problem for the maximum singular number,” in: Trans. Intern. Sci. Conf. “The Issues of Calculation Optimization ISCOPT-XL” devoted to the 90th birthday anniversary of Acad. V. M. Glushkov, Ukraine, Crimea, Katsiveli, Sept. 30–Oct. 4, 2013, V. M. Glushkov Inst. of Cybernetics, NAS of Ukraine, 2013.Google Scholar
  4. 4.
    P. I. Stetsyuk and L. B. Koshlai, “Optimal normalized structure of demand and value added in a productive Leontief model,” Cybern. Syst. Analysis, 46, No. 5, 729–737 (2010).CrossRefMathSciNetGoogle Scholar
  5. 5.
    P. I. Stetsyuk and A. V. Bondarenko, “Spectral properties of the Leontief model,” Teoriya Optim. Reshenii, No. 10, 84–90 (2011).Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.V. M. Glushkov Institute of CyberneticsNational Academy of Sciences of UkraineKyivUkraine
  2. 2.The University of FribourgFribourgSwitzerland

Personalised recommendations