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 ?, ?1, ?2 two positive numbers ??, ??. Necessary sufficient conditions for the existence of solution are given numerical algorithms, using modified unsymmetric Lanczos scheme, reconstruct matrix prescribed data proposed. Some illustrative examples presented. The obtained results extend several existing in literature.