Constructing a unitary Hessenberg matrix from spectral data
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Authors
Gragg, William B.
Ammar, Gregory S.
Reichel, Lother
Subjects
inverse eigenvalue problem
unitary matrix
orthogonal polynomial
unitary matrix
orthogonal polynomial
Advisors
Date of Issue
1988-11
Date
1988-11
Publisher
Monterey, California. Naval Postgraduate School
Language
en_US
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
Type
Technical Report
Description
Series/Report No
Department
Identifiers
NPS Report Number
NPS-53-89-005
Sponsors
prepared in conjunction with research conducted
for the National Science Foundation and for the Naval Postgraduate School Research Council and funded by the Naval Postgraduate School Research Council.
Funder
O&MN, Direct funding
Format
Citation
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.