非负对称矩阵谱半径定理的一个推广

A Generation of Spectral Radius Theorem of Nonnegative Symmetric Matrix

矩阵谱半径与系统稳定性或算法收敛性问题关系十分密切,利用分块矩阵及相关运算性质,将非负对称矩阵谱半径(Perron根)的一个界值定理推广至一般Hermitian矩阵,得到一般Hermitian矩阵谱半径的一个界值定理,在某些特殊情况下推广的界值定理能得到更好的结果.

The relation between spectral radius of matrix and system stability or algorithm convergence is very close.This paper uses block matrix and its related property to generalize one bounded value theorem of spectral radius（ Perron root） of nonnegative symmetric matrix into general Hermitian matrix,and obtains a bounded value theorem of spectral radius of general Hermitian matrix.Under some special conditions,the generalized bounded value theorem can receive better results.