# Accession Number:

## ADA169257

# Title:

## An Algorithm for Rescaling a Matrix Positive Definite.

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## STANFORD UNIV CA SYSTEMS OPTIMIZATION LAB

# Personal Author(s):

# Report Date:

## 1986-04-01

# Pagination or Media Count:

## 26.0

# 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.

# Descriptors:

# Subject Categories:

- Theoretical Mathematics