On the determination of a tridiagonal matrix from its spectrum and a submatrix

Abstract Given a set of 2 n real numbers λ 1 2 2 n , the authors describe the set { S } of n × n tridiagonal matrices with the property that each S can be completed to a 2 n ×2 n tridiagonal matrix L with spec( L )={λ 1 , λ 2 ,…,λ 2 n }.