Constructing a Unitary Hessenberg Matrix from Spectral Data
نویسندگان
چکیده
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 eecient 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.
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