Constructing a Unitary Hessenberg Matrix from Spectral Data
Abstract
We consider the numerical construction of a unitary Hessenberg matrix from spectral data using an inverse QR algorithm. Any unitary upper Hessenberg matrix H with nonnegative subdiagonal elements can be represented by 2n - 1 real parameters. This representation, which we refer to as the Schur parameterization of H, facilitates the development of efficient algorithms for this class of matrices. We show that a unitary upper Hessenberg matrix H with positive subdiagonal elements is determined by its eigenvalues and the eigenvalues of a rank-one unitary perturbation of H. The eigenvalues of the perturbation strictly interlace the eigenvalues of H on the unit circle. Inverse eigenvalue problem, Unitary matrix, Orthogonal polynomial.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 15, 1988
- Accession Number
- ADA204114
Entities
People
- Gregory Ammar
- Lother Reichel
- William Gragg
Organizations
- Naval Postgraduate School