哈密顿矩阵的逆特征值问题  

The Inverse Eigenvalue Problem of Hamiltonian Matrices

作　　者：孟纯军[1] 胡锡炎[2] 

机构地区：[1]中南大学数学科学与计算技术学院,长沙410083 [2]湖南大学数学与计量经济学院,长沙410082

出　　处：《数学物理学报（A辑）》2007年第3期442-448,共7页Acta Mathematica Scientia

基　　金：中国博士后科学基金(20060390888);国家自然科学基金(10571047)资助

摘　　要：该文探讨了哈密顿矩阵的逆特征值问题,得到了有解的充要条件、通解的表达式以及最小范数解．并给出了最佳逼近解的求法．给出了相应的算法,数值实例说明算法是可行的。In this paper the authors mainly discuss the inverse eigenvalue problem of Hamiltonian matrices. The necessary and sufficient conditions of solvability for the problem are conducted. And the general form of solutions is presented. Further, the authors research the optimal approximation solution to any given matrix, prove that such solution is unique and provide the formula to compute it. Some examples are given to demonstrate that the results are right and the algorithm is feasible.

关 键 词：逆特征值问题 哈密顿矩阵 奇异值分解 最佳逼近解 

分 类 号：O241.6[理学—计算数学]