1991 | OriginalPaper | Buchkapitel
Constructing a Unitary Hessenberg Matrix from Spectral Data
verfasst von : Gregory Ammar, William Gragg, Lothar Reichel
Erschienen in: Numerical Linear Algebra, Digital Signal Processing and Parallel Algorithms
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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We consider the numerical construction of a unitary Hessenberg matrix from spectral data using an inverse QR algorithm. Any upper unitary Hessenberg matrix H with nonnegative subdiagonal elements can be represented by 2n − 1 real parameters. This representation, which we refer to as the Schur parametrization 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.