【作者】 李素华；

【导师】 李耀堂；

【作者基本信息】 云南大学 ， 计算数学， 2016， 硕士

【摘要】 随机矩阵作为一类特殊的非负矩阵,具有广泛的应用背景.数理经济学、运筹学和Markov链等众多领域的许多问题都与随机矩阵有着密切的联系.随机矩阵非1特征值的定位与具有非零相同行和实矩阵非奇异的判定条件联系紧密,二者在随机矩阵理论研究中占有重要的地位,是近年来国内外学者研究的热点问题之一.本文继续这些问题的研究,利用修正矩阵理论及S-SDD矩阵的非奇异性,给出了具有非零相同行和实矩阵非奇异的几个新的充分条件,并由其得到了随机矩阵的几个新的非1特征值包含集.数值例子表明,所得结果改进了Cvetkovic et al. [Electronic Transactions on Numerical Analysis,18 (2004) 73-80], Shen et al. [Linear Algebra and its Applications,447 (2014) 74-87] 和Li et al. [Linear and Multilinear Algebra, 11(2015) 2159-2170]的结果.更多还原

【Abstract】 As a special kind of nonnegative matrices, stochastic matrices have extensive application background. Many problems in mathematical economics, operations research and Markov chains and so on all have a close connection with stochastic matrices. Since the localization of all eigenvalues different from 1 is contacted close-ly with nonsingular criteria for real matrices with same nonzero row sums, both of them play important roles in the stochastic matrices theory, which have become one of the hot issues in recent years. In this thesis, we continue to study these problems, on basis of the modified matrices theory and the nonsingularity of S-SDD matrices, some new nonsingular criterias of real matrices with same nonzero row sums are given, and some new inclusion sets of all eigenvalues different from 1 for stochastic matrices are obtained. Numerical examples illustrate that the proposed results are more accurate than the results of Cvetkovic et al. [Electronic Transactions on Nu-merical Analysis,18(2004)73-80], Shen et al. [Linear Algebra and its Applications, 447(2014)74-87] and Li et al. [Linear and Multilinear Algebra,11(2015)2159-2170].更多还原