A fast numerical algorithm for constructing nonnegative matrices with prescribed real eigenvalues
Year: 2013
Type: preprint
Abstract: 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 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.
Source: arXiv (Cornell University)
Author: Lin, Matthew M.
Institution: National Chung Cheng University
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: G8178182781
OpenAlex ID: W2297287764