一类伪Jacobi矩阵的广义双倍维逆特征值问题  

A GENERALIZED DOUBLE DIMENSIONAL INVERSE EIGENVALUE PROBLEM FOR A KIND OF PSEUDO-JACOBI MATRICES

作　　者：胡文宇 徐伟孺 Hu Wenyu;Xu Weiru(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,China)

机构地区：[1]四川师范大学数学科学学院,成都610066

出　　处：《计算数学》2024年第4期469-481,共13页Mathematica Numerica Sinica

基　　金：国家自然科学基金项目(12301484);四川省自然科学基金项目(2022NSFSC1815,24LHJJ0071,2023NSFSC1326)资助.

摘　　要：本文考虑了一类伪Jacobi矩阵的广义双倍维逆特征值问题,该问题通过从矩阵的特征值和它的r阶顺序主子矩阵来重构该矩阵.该类矩阵特征值的分布与其两个互补主子矩阵特征值的大小关系有关,当大小关系不同时,该类矩阵的特征值分布将会发生很大变化.于是根据该矩阵特征方程根的分布情况来讨论其特征值分布,并且给出了问题有解的充分必要条件.然后,将该问题等价转化为蒋尔雄提出的k问题并解决了该问题.最后,通过数值算例验证了所给算法的有效性和可行性.In this paper,we consider the generalized double dimensional inverse eigenvalue problem for a kind of pseudo-Jacobi matrices,which is reconstructed from the eigenvalues of these matrices and their r×r leading principle submatrices.The eigenvalue distribution of this kind of matrices is related to the size relationship between the eigenvalues of two complementary principle submatrices.When the size relationship is different,the eigenvalue distribution of this kind of matrices will change greatly.Therefore,the eigenvalue distribution of these matrices is discussed according to the distribution of the root of the secular equation,and the necessary and sufficient conditions for the problem to have a solution are given.Then the problem is solved by equivalently converting such a problem into the k problem proposed by Erxiong Jiang.Finally,two numerical examples are given to verify the effectiveness and feasibility of the proposed algorithm.

关 键 词：逆特征值问题 重构算法 伪Jacobi矩阵 谱分布 

分 类 号：O151.21[理学—数学]