An Inverse Extremal Eigenproblem for Bordered Tridiagonal Matrices Applied to an Inverse Singular Value Problem for Lefkovitch-Type Matrices

This paper focuses on the inverse extremal eigenvalue problem (IEEP) and a special inverse singular value problem (ISVP). First, a bordered tridiagonal matrix is constructed from the extremal eigenvalues of its leading principal submatrices and an eigenvector. Then, based on the previous construction, a Lefkovitch-type matrix is constructed from a particular set of singular values and a singular vector. Sufficient conditions are established for the existence of a symmetric bordered tridiagonal matrix, while the nonsymmetric case is also addressed. Finally, numerical examples illustrating these constructions derived from the main results are presented.