An Algorithm for Rescaling a Matrix Positive Definite.

Abstract

For a given square real matrix M, we present a general algorithm which decides the existence of a positive diagonal matrix D such that DM is positive definite and which constructs the D if it exists. It is shown that solving this matrix rescaling problem is equivalent to finding a solution of an infinite system of linear inequalities. The algorithm solves the infinite system of linear inequalities by generating and solving a sequence of linear programs. Keywords: Eigenvalues; Eigenvectors.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1986
Accession Number
ADA169257

Entities

People

  • Hui Hu

Organizations

  • Stanford University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algebra
  • Algorithms
  • Computer Programming
  • Contracts
  • Eigenvalues
  • Eigenvectors
  • Evolutionary Algorithms
  • Heuristic Methods
  • Inequalities
  • Linear Algebra
  • Linear Programming
  • Mathematical Programming
  • Operations Research
  • Optimization
  • Security
  • Sequences
  • Simplex Method

Fields of Study

  • Mathematics

Readers

  • Linear Algebra