On Inverse Eigenvalue Problems for Two Kinds of Special Banded Matrices

Abstract

This paper presents two kinds of symmetric tridiagonal plus paw form (hereafter TPPF) matrices,
which are the combination of tridiagonal matrices and bordered diagonal matrices. In particular, we exploit
the interlacing properties of their eigenvalues. On this basis, the inverse eigenvalue problems for the two
kinds of symmetric TPPF matrices are to construct the matrices of their corresponding form, from the
minimal and the maximal eigenvalues of all their leading principal submatrices respectively. The necessary and sucient conditions for the solvability of the problems are derived. Our results are constructive and corresponding numerical algorithms and some examples are given.