【作者】 张荣芳；

【导师】 杨晋；

【作者基本信息】 太原理工大学 ， 应用数学， 2008， 硕士

【摘要】 非负矩阵谱理论在管理科学、数理经济学中有着广泛的应用。本文主要在一些谱理论基础上研究非负矩阵的最大特征值的界的估计和算法问题。主要内容为:1、简单介绍一些特殊非负矩阵的基础知识,简要综述了相关的谱理论。2、研究非负矩阵最大特征值界的估计,探讨了一些较好的结果,得到一种新的估计,并证明了这个估计有较好的精度。3、提出了求不可约非负矩阵最大特征值的一种迭代算法,并证明了该算法的收敛性定理和误差估计,最后通过实例说明了其有效性。更多还原

【Abstract】 The spectral theory of nonnegative matrix is widely used in the areas of Management Science and Mathematics Economics. This paper investigates the estimating the bounds and algorithm for the maximum eigenvalue of nonnegative matrix on the basis of some spectral theories. The main contents are as follows:1、The basic knowledge of some special nonnegative matrices are introduced simply, and the relevant spectral theories are summarized.2、The bounds for the maximum eigenvalue of the nonnegative matrix are studied and some good bounds are considered especially. A new bound of the maximum eigenvalue are obtained, which is proved to be more accurate.3、A iterate method of finding the maximum eigenvalue of irreducible nonnegative matrix is presented, and the convergence theorem and error estimating of this algorithm are proved. At last, two examples are given to show that the new method is effective.更多还原