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逆奇异值问题的一个二阶收敛算法

魏水艳1, 陈小山2   

  1. 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.

魏水艳, 陈小山. 逆奇异值问题的一个二阶收敛算法[J]. 计算数学, 2021, 43(4): 471-483.

Wei Shuiyan, Chen Xiaoshan. A QUADRATICALLY CONVERGENT ALGORITHM FOR INVERSE SINGULAR VALUE PROBLEMS[J]. Mathematica Numerica Sinica, 2021, 43(4): 471-483.

A QUADRATICALLY CONVERGENT ALGORITHM FOR INVERSE SINGULAR VALUE PROBLEMS

Wei Shuiyan1, Chen Xiaoshan2   

  1. 1. Yongzhou Normal College, Yongzhou 425100 China;
    2. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
  • Received:2020-03-25 Online:2021-11-14 Published:2021-11-12
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.
Let$\{A_i\}_{i=0}^n$be$n+1$real matrices with size $m\times n (m\geq n)$and given$n$positive numbers$\{\sigma_i^{*}\}_{i=1}^n$.The purpose of this paper is to study the following inverse singular value problems:find$n$real numbers $\{c_i^{*}\}_{i=1}^n$such that the singular values of the matrix $A_0+c_1^{*}A_1+\cdots+c_n^{*}A_n$are$\{\sigma_i^*\}_{i=1}^n.$ Based on the matrix equations, we propose a new numerical algorithm and analyze that it is of quadratic convergence. The new algorithm can be considered as a generalization of inverse symmetric eigenvalue problems in[Aishima, Linear Algebra and its Applications, 2018, 542:310-333].Numerical experiments show that new algorithm is effective.

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