An Algorithm for Rescaling a Matrix Positive Definite.
STANFORD UNIV CA SYSTEMS OPTIMIZATION LAB
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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.
- Theoretical Mathematics