“Centro-Symmetric Isospectral Flows and Some Inverse Eigenvalue Problems”

This paper is concerned with the solution of some structured inverse eigenvalue problems in the class of centrosymmetric matrices. For this aim, isospectral flows evolving in the space of centrosymmetric matrices are considered to numerically construct a symmetric Toeplitz matrix or a persymmetric Hankel matrix from prescribed eigenvalues. We establish a link between the two problems and we investigate the use of simultaneously diagonalizable algebra based on sine transform [Linear Algebra Appl. 52/53 (1983) 992] to choose the starting centrosymmetric matrices for the isospectral flows. Some numerical tests show that our approach can tackle both problems when the solvability is guaranteed and it can give good insights when the existence of the solution is not guaranteed.