关于完全正矩阵的几点注记(英文)  

Some Remarks on Completely Positive Matrices

作　　者：徐常青[1] 

机构地区：[1]安徽大学数学系,合肥230039

出　　处：《工科数学》2000年第3期22-27,共6页Journal of Mathematics For Technology

基　　金：Supported by Anhui Educational Committee( 99JL0 0 0 9)

摘　　要：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.

关 键 词：完全正矩阵 弱对角占优矩阵 分解指数 上界 

分 类 号：O151.21[理学—数学]