Inverse Eigenvalue Problem of Unitary Hessenberg Matrices

Abstract EN

Let H∈ℂn×n be an n×n unitary upper Hessenberg matrix whose subdiagonal elements are all positive, let Hk be the kth leading principal submatrix of H, and let H˜k be a modified submatrix of Hk.

It is shown that when the minimal and maximal eigenvalues of H˜k (k=1,2,…,n) are known, H can be constructed uniquely and efficiently.

Theoretic analysis, numerical algorithm, and a small example are given.