An inverse eigenvalue problem for doubly periodic pseudo-Jacobi matrices

In this paper, we investigate a direct and an inverse eigenvalue problem to recover doubly periodic pseudo-Jacobi matrices from three spectra λ, μ1, μ2 and two positive numbers β⋆, β♢. Necessary and sufficient conditions for the existence of solution are given and numerical algorithms, using a modified unsymmetric Lanczos scheme, to reconstruct the matrix from the prescribed data are proposed. Some illustrative numerical examples are presented. The obtained results recover and extend several existing results in the literature.