求解逆特征值问题的全局性非精确牛顿类方法  

A globally convergent inexact Newton-like method for solving inverse eigenvalue problems

作　　者：沈卫平 王悦 SHEN Weiping;WANG Yue(College of Mathematics and Computer Science,Zhejiang Normal University,Jinhua 321004,China)

机构地区：[1]浙江师范大学数学与计算机科学学院,浙江金华321004

出　　处：《浙江师范大学学报（自然科学版）》2022年第3期275-283,共9页Journal of Zhejiang Normal University:Natural Sciences

基　　金：国家自然科学基金资助项目(12071441)。

摘　　要：为了研究求解逆特征值问题的全局性算法,利用反幂法获得近似特征向量,提出了一种求解逆特征值问题的全局性非精确牛顿类算法.在一定的条件下,给出了该全局算法的收敛性分析,并且证明了该算法的超线性/二阶收敛性质.最后,通过数值例子进一步验证所提出算法的全局收敛性.In order to study the global algorithm for solving inverse eigenvalue problems,a global inexact Newton-like algorithm for solving inverse eigenvalue problems was proposed by using the inverse power method to obtain approximate eigenvectors.The convergence analysis of the global algorithm was given under certain conditons,the superlinear/second-order convergence properties of the algorithm were proved.The global convergence of the proposed algorithm was further verified by numerical examples.

关 键 词：逆特征值问题 非精确牛顿类方法 反幂法 全局收敛性 

分 类 号：O241.7[理学—计算数学]