A direct solution to the stochastic inverse eigenvalue problem for complex-valued eigenspectra
type: Item
instance of: scholarly article
title: A direct solution to the stochastic inverse eigenvalue problem for complex-valued eigenspectra
zbMATH Open document ID: 1504.15067
author: André M. McDonald
author: Michaël Antonie Van Wyk
author: Guanrong Chen
published in: Linear Algebra and its Applications
publication date: 2022-12-08T00:00:00Z
review text: The authors give a direct solution to the stochastic inverse eigenvalue problem, i.e., constructing a stochastic matrix with prescribed spectrum. The solution uses Markov state disaggregation to construct a Markov chain with the associated stochastic transition matrix having the required spectrum. Unlike numerical methods that minimize a cost function, the advantage of the construction is that it can be achieved in a finite and predetermined number of iterations. The novel solution generalizes the original technique of \textit{L. Ciampolini} et al. [``Direct solution of the inverse stochastic problem through elementary Markov state disaggregation'', Preprint, \url{https://hal.archives-ouvertes.fr/hal-01016804}]. Example of \(4\times 4\) and \(5\times 5\) matrices are given to illustrate the construction.
Mathematics Subject Classification ID: 15A29
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15B51
zbMATH DE Number: 7628676
zbMATH Keywords: inverse eigenvalue problem
zbMATH Keywords: inverse stochastic problem
zbMATH Keywords: stochastic matrix
zbMATH Keywords: Markov state disaggregation
reviewed by: Tin-Yau Tam
MaRDI profile type: Publication
full work available at URL: j.laa.2022.11.005
OpenAlex ID: W4309736088
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DOI: 10.1016/J.LAA.2022.11.005
description: scientific article; zbMATH DE number 7628676