重庆工商大学学报：自然科学版
重慶工商大學學報：自然科學版
중경공상대학학보：자연과학판
Journal of Chongqing Technology and Business University:Natural Science Edition
2012年
4期
11-16
,共6页
非负矩阵%广义Perron补%不可约性%Perron根
非負矩陣%廣義Perron補%不可約性%Perron根
비부구진%엄의Perron보%불가약성%Perron근
nonnegative matrices%generalized Perron complement%irreducibility%Perron root
矩阵的谱半径在特征值估计理论、广义逆矩阵、数值分析以及矩阵序列、矩阵级数的收敛分析、控制理论中都有着极为重要的作用，近年来许多学者都致力于这方面的研究，提出了许多改进的谱半径估计方法，利用Perron补矩阵进行谱半径估计也一直受到广大学者的重视．通过研究矩阵的广义Perron补的性质，给出非负矩阵Perron根界的几个新的估计式．
矩陣的譜半徑在特徵值估計理論、廣義逆矩陣、數值分析以及矩陣序列、矩陣級數的收斂分析、控製理論中都有著極為重要的作用，近年來許多學者都緻力于這方麵的研究，提齣瞭許多改進的譜半徑估計方法，利用Perron補矩陣進行譜半徑估計也一直受到廣大學者的重視．通過研究矩陣的廣義Perron補的性質，給齣非負矩陣Perron根界的幾箇新的估計式．
구진적보반경재특정치고계이론、엄의역구진、수치분석이급구진서렬、구진급수적수렴분석、공제이론중도유착겁위중요적작용，근년래허다학자도치력우저방면적연구，제출료허다개진적보반경고계방법，이용Perron보구진진행보반경고계야일직수도엄대학자적중시．통과연구구진적엄의Perron보적성질，급출비부구진Perron근계적궤개신적고계식．
Spectral radius of matrix plays an extremely important role in characteristic value estimation theory, generalized inverse matrix, numerical analysis, matrix sequence, matrix series convergence analysis and control theory, so that in recent years,many scholars are committed to conduct research in this area and put forward a number of improved spectral radius estimation methods. It is widely valued by a great many of scholars to use generalized Perron complement matrix to estimate spectral radius. By studying the properties of generalized Perron complement, this paper gives several new estimation expressions of Perron root bound.
