一类二次算子族的数值域的MATLAB图形实现  

MATLAB Graph Realization of the Numerical Range of a Class of Quadratic Operator Pencil

作　　者：邢利刚 张新艳 XING Li-gang;ZHANG Xin-yan(The Statistics and Mathematics Department of Financial and Economic Inner Mongolar University,Hohhot,010071)

机构地区：[1]内蒙古财经大学统计与数学学院,呼和浩特010071

出　　处：《现代计算机》2020年第24期46-48,共3页Modern Computer

基　　金：内蒙古自治区教育厅科研项目(No.NJZY133)。

摘　　要：算子的数值域是算子理论的一个重要工具,利用算子的数值域可以对算子的谱进行估计。在文献[1]中我们利用算子数值域的理论得到一类二次算子族的谱估计关系,并给出该类二次算子族数值域的分部特征及其具体描述形式。利用MATLAB软件对M, K, A取不同类型的复数矩阵时的二次算子族L(λ)=Mλ2-iKλ-A的数值域进行描绘,从图形的结果来看,这些二次算子族的数值域都关于虚轴对称,因为对矩阵算子来说,谱问题主要就是特征值问题,通过计算和图形很好地验证我们的结果。The numerical range of operators is an important tool of operator theory.The spectrum of operators can be estimated by using the numerical range of operators.In paper[1],we obtain the spectral estimation relation of a class of quadratic operator pencil by using the theory of the numerical domain of operators,and give the partial characteristics and the specific description form of the numerical range of this kind of quadratic operator pencil.In this paper,we use MATLAB software to draw the graph of this quadratic operator pencil L(λ)=Mλ2-iKλ-A,when M,K,A are different complex matrices.From the results of graphs,the numerical fields of these quadratic operator pencils are all symmetric to virtual axisymmetric.For matrix operators,the spectrum problem is the eigenvalue problem.These pictures are well verified our results.

关 键 词：二次算子族 数值域 MATLAB绘图 

分 类 号：O177[理学—数学] TB115[理学—基础数学]