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The inverse generalized eigenvalue problem for generalized jacobi matrices

This paper presents the following inverse eigenvalue problem for generalized Jacobi matrices: Give two 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 two characteristic pairs are the characteristic pairs of the inverse generalized eigenvalue problem. The paper discussed the existence and uniqueness of the question's solution. And the expression of the solution of the problem is given, and some numerical example is provided.