A direct solution to the stochastic inverse eigenvalue problem for complex-valued eigenspectra
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.
scientific article; zbMATH DE number 7628676
scientific article