ABSTRACT

Constructing a matrix by its spectral information including singular values is called inverse singular value problem (ISVP). In this paper, an ISVP for nonsymmetric ahead arrow matrix by two eigenpairs of the required matrix and one singular value of each leading principal submatrices is investigated. To solve the problem, the recurrence relation of characteristic polynomial of the block Jordan–Weilant matrix associated with the aim matrix is obtained. The conditions of solvability of the problem are derived. Finally a numerical algorithm and an example are given.

中文翻译：

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非对称前进箭头矩阵的逆奇异值问题

摘要

通过包含奇异值的频谱信息构建矩阵称为逆奇异值问题 (ISVP)。本文研究了由所需矩阵的两个特征对和每个前导主子矩阵的一个奇异值组成的非对称前向箭头矩阵的ISVP。为了解决这个问题，得到了与目标矩阵相关联的块Jordan-Weilant矩阵的特征多项式的递推关系。推导出问题的可解性条件。最后给出了一个数值算法和一个例子。