关于完全正矩阵的几点注记(英文)

Some Remarks on Completely Positive Matrices

本文给出了一个 n×n非负、对称、弱对角占优矩阵 A为完全正的一个充分条件 .我们还给出了较好的算法 ,用以获得关于矩阵 A(当 A为完全正时 )的分解指数的一个上界 .

A nonnegative n×n positive semidefinite matrix A is called doubly nonnegative, and A is called completely positive if A can be factored as A=BB′ for some (not necessarily square) entrywise nonnegative matrix B. The smallest number of columns of B is called the factorization index of A. This paper presents a sufficient condition for a weakly diagonally dominant nonnegative symmetric matrix to be completely positive. Also a revised algorithm is presented for obtaining a better upper bound for its factorization index.