逆奇异值问题的一个二阶收敛算法

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AishimaLinear 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.

A QUADRATICALLY CONVERGENT ALGORITHM FOR INVERSE SINGULAR VALUE PROBLEMS

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 inAishima, Linear Algebra and its Applications, 2018, 542:310-333].Numerical experiments show that new algorithm is effective.