吉林大学学报（理学版）2017，Vol.55Issue(1)：33-37,5.DOI:10.13413/j.cnki.jdxblxb.2017.01.06
基于正交投影方法的二次特征值反问题及其最佳逼近解
Inverse Quadratic Eigenvalue Problem and Its Optimal Approximation Solution Based on Orthogonal Projection Methods
摘要
Abstract
We considered the generalized centrosymmetric solution (generalized anti-centrosymmetric solution)of an inverse quadratic eigenvalue problem and its optimal approximation problem.By using the orthogonal projection methods of matrix,we gave the solution of matrix equation AX +BY+CZ=0 and its optimal approximation problem.According to the properties of generalized centrosymmetric matrices (generalized anti-centrosymmetric matrices),we derived the conditions for the problem with a generalized centrosymmetric solution (generalized anti-centrosymmetric solution)and the expression of general solution. We proved the existence and the uniqueness of solution of the optimal approximation problem,and obtained the expression of the optimal approximation solution.关键词
二次特征值反问题/广义中心对称矩阵/最佳逼近解/正交投影方法Key words
inverse quadratic eigenvalue problem/generalized centrosymmetric matrix/optimal approximation solution/orthogonal projection method分类
数理科学引用本文复制引用
周硕,白媛..基于正交投影方法的二次特征值反问题及其最佳逼近解[J].吉林大学学报（理学版）,2017,55(1):33-37,5.基金项目
国家自然科学基金(批准号:11072085)和吉林省自然科学基金(批准号:201115180). （批准号:11072085）
