摘要
将著名的一元控制不等式推广到多元的情形,获得了一个重要的多元凸函数的控制不等式。引入了广义多元凸函数概念,并且给出了一个实用而简洁的广义多元凸函数的判据。作为多元凸函数的控制不等式在矩阵方面的初步应用,获得了矩阵特征值和奇异值的简洁的控制不等式。
The well-known majorizing inequality is generalized to space of higher dimensions, and a important majorizing inequality is obtained. The concept of generalized convex function of several variables is introduced. A material criterion is given. As applications of majorizing inequality of convex function of several variables, some majorizing inequalities of eigenvalue and singular value of matrix are obtained.
出处
《科学技术与工程》
2005年第21期1581-1585,1589,共6页
Science Technology and Engineering
基金
国家973计划项目(2004CB318003)资助
关键词
广义多元凸函数
控制不等式
矩阵
特征值
奇异值
generalized convex function of several variables majorizing inequalities matrix eigenvalue singular value
