基于偏序集不动点理论的矩阵方程可解性研究

摘要

In this paper,a new fixed point theorem in partially order sets is proposed.Based on this fixed point theorem,we proved that the matrix equation X-m∑i=1 A*iXδiAi =Q (0 ＜ δi ＜ 1) always has a unique Hermitian positive definite (HPD) solution without any restrictions on coefficient matrices.%首先构造了一个偏序集中的新的不动点定理,然后基于此不动点定理,证明了矩阵方程X-mi=1∑A*iXδiAi=Q(0＜δi＜1)总是存在唯一的Hermite正定解.