The problem of constructing an n by n Jacobi matrix J with prescribed spectrum {λi}n1, such that the submatrix J(ρ), obtained from J by deleting its ρth row and column, also has a prescribed spectrum {𝜇i}n-11 is studied. The cases ρ=1 and ρ=n are well known. For the case 2 ≤ ρ ≤ n-1 it is shown that the problem has a unique solution under the condition λi < 𝜇i < λi+1, i=1, 2, . . . , n-1.
@article{1840,
title = {On the construction of Jacobi matrices from spectral data},
journal = {CUBO, A Mathematical Journal},
year = {1988},
language = {en},
url = {http://dml.mathdoc.fr/item/1840}
}
Rojo J., Oscar; Soto, Ricardo. On the construction of Jacobi matrices from spectral data. CUBO, A Mathematical Journal, (1988), . http://gdmltest.u-ga.fr/item/1840/