A kind of inverse generalized eigenvalue problem for generalized periodic seven-diagonal matrices

This paper deals with the following generalized inverse eigenvalue problem for generalized seven-diagonal matrix: give three characteristic pairs and a matrix, get a generalized Jacobi matrix (That is the product of secondary diagonal elements of the Jacobi matrix is positive). Let the three characteristic pairs are the characteristic pairs of the inverse generalized eigenvalue problem. The algorithm, uniqueness theorem of the solution of the problem and The expression of the solution of the problem are given, and some numerical example is provided.