\(m\)-functions and inverse generalized eigenvalue problem (Q2720380)

The author deals with the inverse generalized eigenvalue problem \((Ax=\lambda Bx\), where \(A\) is a Jacobi matrix with positive elements at the lower and upper diagonal and where \(B\) is a diagonal matrix with non-zero elements) by means of the concept of \(m\)-functions.NEWLINENEWLINENEWLINERelated treatments of the problems can be found in the paper of \textit{A. Alaca} and \textit{A. B. Mingarelli} [Lect. Notes Pure Appl. Math. 191, 135-148 (1997; Zbl 0877.15011)] for \(B\) indefinite, in the paper of \textit{H. Hald} [Linear Algebra Appl. 14, 63-85 (1976; Zbl 0328.15007)] for \(B\) being the identity matrix, and in the paper of \textit{K. Ghanvari} and \textit{A. Mingarelli} [Generalized inverse eigenvalue problem for symmetric matrices, Int. J. Appl. Math. 4, 199-209 (2000)] for \(A\) and \(B\) symmetric matrices or \(A\) and \(B\) Jacobi matrices with \(B\) positive definite.