一类伪Jacobi矩阵的保结构构造算法  

A structure-preserving construction algorithm for a kind of pseudo-Jacobi matrices

作　　者：徐伟孺 蒲会 彭欢 沈芮西 XU Weiru;PU Hui;PENG Huan;SHEN Ruixi(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,四川成都610066

出　　处：《安徽大学学报(自然科学版)》2025年第2期20-27,共8页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(12301484);四川省自然科学基金资助项目(2022NSFSC1815,2024NSFSC2041);四川师范大学大学生创新创业训练计划项目(S202310636114);四川师范大学2023年度人才培养质量和教学改革校级项目(20230095XKC)。

摘　　要：研究了一类伪Jacobi矩阵的逆特征值问题.通过探讨该伪Jacobi矩阵的谱分布性质,提出了该问题的一种新的表述形式.随后,研究了该问题解的唯一性,给出了有解的充要条件和具体的保结构构造算法.最后,通过数值算例验证了该问题解的唯一性及算法的可行性.This paper investigated the inverse eigenvalue problem of a class of pseudo-Jacobi matrices.A new formulation of this problem was proposed by exploring the spectrum distribution properties of pseudo-Jacobi matrices.Subsequently,the uniqueness of solutions to this kind of problem was studied,and the necessary and sufficient conditions and the concrete structure-preserving construction algorithm were given.Finally,the uniqueness of the solution to the problem and the feasibility of the proposed algorithm were verified by numerical examples.

关 键 词：伪Jacobi矩阵 保结构算法 逆特征值问题 谱分布 

分 类 号：O157.5[理学—数学]