The Generalized Inverse Eigenvalue Problem for Generalized Periodic Jacobi Matrices

摘要

This paper presents the following inverse eigenvalue problem for generalized periodic Jacobi matrices:=given real numbers λ, μ, nonzero vectors x, y ∈ R~n and a real matrix B. Find n×n real generalized periodic Jacobi matrices J (c_i = kb_i, k > 0, i = 1, ..., n) such that Jx = λBx, Jy = μBy. 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.