a School of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha, Hunan 410076, PR China b Department of Mathematics, University of Minho, Campus de Gualtar, 4710-057 Braga, Portugal
Abstract:
We propose an algorithm for solving the inverse eigenvalue problem for real symmetric block Toeplitz matrices with symmetric Toeplitz blocks. It is based upon an algorithm which has been used before by others to solve the inverse eigenvalue problem for general real symmetric matrices and also for Toeplitz matrices. First we expose the structure of the eigenvectors of the so-called generalized centrosymmetric matrices. Then we explore the properties of the eigenvectors to derive an efficient algorithm that is able to deliver a matrix with the required structure and spectrum. We have implemented our ideas in a Matlab code. Numerical results produced with this code are included.