关于两类特殊矩阵2-范数界的估计  

Estimation of 2-norm bounds for two types of special matrices

作　　者：张超 邓勇 ZHANG Chao;DENG Yong(College of Mathematics and Statistics,Kashi University,Kashi 844006,China;Research Center of Modern Mathematics and Its Application,Kashi University,Kashi 844006,China)

机构地区：[1]喀什大学数学与统计学院,新疆喀什844006 [2]喀什大学现代数学及其应用研究中心,新疆喀什844006

出　　处：《青海师范大学学报（自然科学版）》2024年第3期55-59,68,共6页Journal of Qinghai Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(12061039)。

摘　　要：矩阵的2-范数是对矩阵进行度量的一种方法,它在数值计算、优化问题、机器学习等领域都具有重要的应用.为此,首先推导了Pell和Pell-Lucas数的几个平方和公式.其次分别构造了以Pell或Pell-Lucas数为元素的Hankel-Hessenberg矩阵和Toeplitz-Hessenberg矩阵.最后讨论了这两类矩阵的2-范数的上下界.The 2-norm of a matrix is a method of measuring matrices,which has important applications in numerical calculations,optimization problems,machine learning,and other fields.Therefore,firstly,several square sum formulas of Pell and Pell-Lucas numbers are derived.Secondly,Hankel-Hessenberg and Toeplitz-Hessenberg matrices with Pell or Pell-Lucas numbers as elements are constructed.Finally,the upper and lower bounds of the 2-norm of two matrices are discussed.

关 键 词：Pell数 Pell-Lucas数 Hankel-Hessenberg矩阵 Toeplitz-Hessenberg矩阵 HADAMARD积 2-范数 

分 类 号：O151.21[理学—数学]