复矩阵数值特征及复系数多项式根的定位研究

发布时间：2018-01-14 18:12

本文关键词：复矩阵数值特征及复系数多项式根的定位研究　出处：《重庆大学》2016年硕士论文　论文类型：学位论文

【摘要】：矩阵理论及多项式理论在近代数学、物理学、化学、运筹学与控制论、生物学、动力系统、图像处理等领域有着广泛的应用。本文主要研究矩阵特征值、展形及复系数多项式根的估计与定位问题,其主要内容和创新点包括:(1)应用凸函数的性质及数理统计中的绝对中心距概念得到任意矩阵A的特征值1 2,nll(43)l在如下圆盘区域内:其中(2)由(1)特征值的估计定位给出一些判定Hermite矩阵正定的充分条件;(3)由(1)的特征值估计得到任意复矩阵展形的一个新的上界估计式;(4)由数值形式的Young不等式,给出一些关于矩阵展形下界的估计式;(5)利用实系数多项根的估计给出复系数多项式特征根的新估计区域。
[Abstract]:Matrix theory and polynomial theory are widely used in modern mathematics, physics, chemistry, operational research and cybernetics, biology, dynamic system, image processing and so on. Estimation and location of polynomial Roots with spanned and complex coefficients. Its main contents and innovations include: (1) using the properties of convex function and the concept of absolute center distance in mathematical statistics, the eigenvalue of arbitrary matrix A is obtained. Nll(43)l is located in the following disk region: 2) some sufficient conditions for determining the positive definite of Hermite matrix are given by the estimation of the eigenvalue of Hermite. A new upper bound estimator is obtained from the eigenvalue estimation of arbitrary complex matrix. 4) from the Young inequality in numerical form, we give some estimations about the lower bound of matrix extension. 5) by using the estimator of real coefficient multinomial roots, a new estimation region of polynomial characteristic roots with complex coefficients is given.
【学位授予单位】：重庆大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O151.21

【相似文献】