一类二次特征值反问题及其最佳逼近  

A Classof Inverse Monic Quadratic Eigenvalue Problem

作　　者：周硕[1] 白媛[1] Zhou Shuo Bai Yuan(Science College, Northeast Electric Power University ,Jilin Jilin 132012)

机构地区：[1]东北电力大学理学院,吉林吉林132012

出　　处：《东北电力大学学报》2017年第5期96-101,共6页Journal of Northeast Electric Power University

基　　金：国家自然科学基金项目(11072085);吉林省自然科学基金项目(201115180)

摘　　要：讨论实双反对称矩阵和实双对称矩阵的二次特征值反问题及其最佳逼近问题,利用矩阵的奇异值分解,建立了二次特征值反问题解的充要条件,并给出了其解集的一般表达式。进而考虑了其最佳逼近问题的存在性与唯一性,得到了最佳逼近解的表达式。The paper concerns the quadratic inverse eigenvalue problem of real double symmetric matrix and real double antisymmetric matrix and it＇ s optimal approximation problem. A necessary and sufficient condition for the solution of the quadratic inverse eigenvalue problem is constructed by singular value decomposition of matrix, the general expression of the solution to the problem is provided. Then the existence and uniqueness of the optimal approximation problem is discussed and the expression is provided for the optimal approximation problem.

关 键 词：二次特征值反问题 双对称矩阵 双反对称矩阵 最佳逼近 奇异值分解 

分 类 号：O241.6[理学—计算数学]