The Growth of Powers of a Non-Negative Matrix.

Abstract

Let A be a non-negative nxn matrix. In this paper the growth of the powers A to the M power, m = 1,2,3,... is studied. These powers occur naturally in an iteration process which is important in applications and numerical techniques. Roughly speaking, the asymptotic behavior of each entry of A to the m power is analyzed. The main result is applied to determine necessary and sufficient conditions for the convergence to the spectral radius of A of certain ratios naturally associated with the iteration above.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1979
Accession Number
ADA077094

Entities

People

  • Hans Schneider
  • Shmuel Friedland

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Approximation (Mathematics)
  • Convergence
  • Equations
  • Graphs
  • Iterations
  • Mathematics
  • North Carolina
  • Self Assembly
  • Triangles
  • Universities
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Linear Algebra