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An Algorithm for Rescaling a Matrix Positive Definite

Stanford University. Systems Optimization LaboratoryHui Hu

出版	Stanford University. Systems Optimization Laboratory, 1986
URL	http://books.google.com.hk/books?id=nhoJAAAAIAAJ&hl=&source=gbs_api

註釋

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.