Isospectral flows and the inverse eigenvalue problem for Toeplitz matrices (Q1807764)

The paper is devoted to the inverse eigenvalue problem for Toeplitz matrices that is a real symmetric Toeplitz matrix has to be constructed from prescribed eigenvalues. To solve the problem numerically, a known approach is used, based on isospectral flow solutions, whose equilibria are symmetric Toeplitz matrices. The authors show new properties of the isospectral flow. The case \(n=3\) is studied analytically using a new approach. Global convergence of the iteration process to a regular Toeplitz matrix is proved when starting from a tridiagonal symmetric and centro-symmetric matrix. Numerical experiments confirm the theoretical results and suggest their extension in higher dimension.