CONSTRUCTING TRIDIAGONAL MATRICES WITH PARTIAL EIGENDATA

Constructing a matrix with its total or partial spectral information is called an inverse eigenvalue problem (IEP). In this paper, an IEP for tridiagonal matrices, called TIEP, is studied. TIEP concerns constructing a tridiagonal matrix with real eigenvalues by the extreme eigenvalues of each of the leading principal submatrices, and one eigenpair of the required matrix. Two specific cases of TIEP where the required matrix entries are non-negative, and positive definite have been discussed and the conditions for the solvability of each case are derived.