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INVERSE EIGENVALUE PROBLEM FOR JACOBI MATRICES
Dai Hua
CHINESE JOURNAL OF COMPUTATIONAL PHYSICS
1994, 11 (4):
451-456.
The following inverse eigenvalue problem for Jacobi matrices is considered: Problem IEP.Given λ,μ∈R(λ<μ and x,y∈Rn,x≠0,y≠0, find n×n Jacobi matrix J such that (λ,x) and (μ,y) are exactly the i-th and j-th (i≠j) eigenpairs of the Jacobi matrix J, respectively. The eigenanalysis of Jacobi matrices is given. The necessary and sufficient condition is obtained for one eigenpair to be exactly the i-th eigenpair of a Jacobi matrix. Some necessary and sufficient conditions for existence of solution of the Problem IEP are given.
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