魏水艳¹, 陈小山²

1. 永州师范高等专科学校, 永州 425100;
2. 华南师范大学数学科学学院, 广州 510631

收稿日期:2020-03-25出版日期:2021-11-14发布日期:2021-11-12


基金资助:国家自然科学基金面上项目（11771159）和粤港澳应用数学中心项目（2020B1515310013）资助.

A QUADRATICALLY CONVERGENT ALGORITHM FOR INVERSE SINGULAR VALUE PROBLEMS

Wei Shuiyan¹, Chen Xiaoshan²

1. Yongzhou Normal College, Yongzhou 425100 China;
2. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China

Received:2020-03-25Online:2021-11-14Published:2021-11-12







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设$n+1$个$m\times n（m\geq n）$实矩阵$\{A_i\}_{i=0}^n$和给定的$n$个正数$\{\sigma_i^{*}\}_{i=1}^n$.本文研究如下的逆奇异值问题：求$n$个实数$\{c_i^{*}\}_{i=1}^n$，使得矩阵$A_0+c_1^{*}A_1+\cdots +c_n^{*}A_n$有奇异值$\{\sigma_i^*\}_{i=1}^n.$基于矩阵方程，我们给出了求解逆奇异值问题的一个新的算法，并证明了它的二阶收敛特性.该算法可以看成是Aishima[Linear Algebra and its Applications，2018，542：310-333]中逆对称特征值问题算法的推广.数值例子表明算法的有效性.
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