二次特征值反问题的对称次反对称解及其最佳逼近  

Symmetric and Skew Anti-symmetric Solution of Inverse Quadratic Eigenvalue Problem and Its Optimal Approximation

作　　者：郭丽杰[1] 周硕[1] 

机构地区：[1]东北电力大学理学院,吉林吉林132012

出　　处：《吉林大学学报（理学版）》2009年第6期1185-1190,共6页Journal of Jilin University:Science Edition

基　　金：吉林省科技发展计划项目基金(批准号:20030106)

摘　　要：利用矩阵的奇异值分解和矩阵的Kronecker乘积,讨论构造对称次反对称矩阵M,C和K,使得二次约束Q（λ）=λ^2M＋λC＋K具有给定特征值和特征向量的特征值反问题.首先证明反问题是可解的,并给出了解集SMCK的通式.进而考虑了解集SMCK中对给定矩阵（M,C,K）的最佳逼近问题,得到了最佳逼近解.The inverse eigenvalue problem of constructing symmetric and skew anti-symmetric matrices M,C and K of size n for the quadratic pencil Q（λ）=λ^2M＋λC＋K so that Q（λ） has a prescribed subset of eigenvalues and eigenvectors was considered by means of singular value decomposition of matrix and Kronecker product of matrices.The problem was firstly improved to be solvable and the general expression of the solution to the problem was provided.The optimal approximation problem associated with SMCK was posed,that is,tofind the nearest triple matrix （M, C,K） from SMCK. The existence and uniqueness of the optimal approximation problem was diseussed and the exoression was provided for the optimal approximation problem.

关 键 词：二次特征值 对称次反对称矩阵 反问题 最佳逼近 奇异值分解 

分 类 号：O242.25[理学—计算数学]