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中文摘要：
讨论了一类矩阵的逆奇异值问题.给定非负实数1σ,2σ,…,nσ,两非零实向量x=（x1,x2,…,xm）T,y=（y1,y2,…,yn）T,求m×n阶实矩阵A,使得1σ,2σ,…,σn为A的奇异值,并且x,y分别为A的左右奇异向量.基于Householder变换和矩阵秩1的修正方法得到了问题的算法,而且算法比较经济且易于并行,同时给出了相应的数值例子.
英文摘要：
In this paper,we consider a kind of matrix inverse singular value problem.Given nonnegative numbers σ1,σ2,…,σn,two nonzero real vectors x=（x1,x2,…,xm）T,y=（y1,y2,…,yn）T,find m×n real matrix A,such that σ1,σ2,…,σn are the singular values of A,and x,y are the left and right singular vectors,respectively.Based on Householder transformation and rank-one updating matrices,we propose an algorithm which is economical and easily to parallel to solve the inverse singular value problem.We also give the corresponding numerical example.
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