A method of calculating the spectral radius of a nonnegative matrix and its applications

被引：0
|
作者：
Ibragimov, M [1 ]
机构：
[1] Tashkent State Econ Univ, Tashkent 700063, Uzbekistan
来源：
ECONOMIC THEORY | 2001年 / 17卷 / 02期
关键词：
Leontief model; productiviy; market equilibrium; spectral radius; M-matrices; geometric programming;
D O I：
10.1007/PL00004114
中图分类号：
F [经济];
学科分类号：
02 ;
摘要：
We present a method of calculating the maximal eigenvalue of an indecomposable nonnegative matrix, which is based on ideas of geometric programming. In addition to that, we obtain estimates for elements of an indecomposable nonnegative matrix by its spectral radius. The results make it possible to obtain new necessary conditions for the productivity of the matrix of coefficients in the Leontief input-output model and have the immediate relation to the analysis of M- matrices. Another interesting application of the developed method is given by conditions of stability of the dynamic system of market equilibrium.
引用
收藏
页码：467 / 480
页数：14
相关论文
共 50 条
  • [41] ON A CLASS OF METHODS FOR THE COMPUTATION OF THE SPECTRAL-RADIUS AND THE PERRON VECTOR OF A NONNEGATIVE, IRREDUCIBLE MATRIX
    SANTOS, MC
    LINEAR ALGEBRA AND ITS APPLICATIONS, 1987, 92 : 209 - 223
  • [42] A New Estimate for the Spectral Radius of Nonnegative Tensors
    Cui, Jingjing
    Peng, Guohua
    Lu, Quan
    Huang, Zhengge
    FILOMAT, 2018, 32 (10) : 3409 - 3418
  • [43] Nonnegative matrix factorization and its applications in pattern recognition
    LIU Weixiang*
    Chinese Science Bulletin, 2006, (01) : 7 - 18
  • [44] Optimization of the spectral radius of a product for nonnegative matrices
    Axtell, Jonathan
    Han, Lixing
    Hershkowitz, Daniel
    Neumann, Michael
    Sze, Nung-Sing
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 430 (5-6) : 1442 - 1451
  • [45] Spectral radius of some special nonnegative matrices
    Nazari, A.M.
    Parval, S.
    World Academy of Science, Engineering and Technology, 2010, 69 : 69 - 70
  • [46] ON THE SPECTRAL RADIUS OF HADAMARD PRODUCTS OF NONNEGATIVE MATRICES
    Chen, Dongjun
    Zhang, Yun
    BANACH JOURNAL OF MATHEMATICAL ANALYSIS, 2015, 9 (02): : 127 - 133
  • [47] Spectral radius of some special nonnegative matrices
    Nazari, A.M.
    Parval, S.
    World Academy of Science, Engineering and Technology, 2010, 70 : 69 - 70
  • [48] On sharp bounds for spectral radius of nonnegative matrices
    Lin, Hongying
    Zhou, Bo
    LINEAR & MULTILINEAR ALGEBRA, 2017, 65 (08): : 1554 - 1565
  • [49] New bounds for the spectral radius for nonnegative tensors
    Li, Lixia
    Li, Chaoqian
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2015,
  • [50] Some bounds for the spectral radius of nonnegative tensors
    Li, Wen
    Ng, Michael K.
    NUMERISCHE MATHEMATIK, 2015, 130 (02) : 315 - 335
12345