Fast Recursive Algorithm For Constructing Nonnegative Matrices With Prescribed Real Eigenvalues
Fast Recursive Algorithm For Constructing Nonnegative Matrices With Prescribed Real Eigenvalues
复制标题
DOI：
--
复制
发表时间：
2013-05
期刊：
影响因子：
--
通讯作者：
Matthew M. Lin
中科院分区：
文献类型：
--
作者：
Matthew M. Lin
求解非负矩阵的逆特征值问题的研究已经存在了几十年。显然，如果所需矩阵不限于某种结构，则逆特征值问题是微不足道的。在提供实数谱的情况下，本文提出了一种基于归纳原理的快速数值程序，用于解决两类逆特征值问题，一种针对非负矩阵，另一种针对对称非负矩阵。作为直接应用，我们的方法不仅可以为解决非负或对称非负矩阵的反特征值问题提供充分条件，而且可以为解决随机矩阵的反特征值问题提供快速的数值方法。针对相对较大规模的问题提供了数值示例。
The study of solving the inverse eigenvalue problem for nonnegative matrices has been around for decades. It is clear that an inverse eigenvalue problem is trivial if the desirable matrix is not restricted to a certain structure. Provided with the real spectrum, this paper presents a fast numerical procedure, based on the induction principle, to solve two kinds of inverse eigenvalue problems, one for nonnegative matrices and another for symmetric nonnegative matrices. As an immediate application, our approach can offer not only the sufficient condition for solving inverse eigenvalue problems for nonnegative or symmetric nonnegative matrices, but also a quick numerical way to solve inverse eigenvalue problem for stochastic matrices. Numerical examples are presented for problems of relatively larger size.