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TW 465
Steven Delvaux, Marc Van Barel
Eigenvalue computation for unitary rank structured matrices
Abstract
In this paper we describe how to compute the eigenvalues of a unitary rank structured matrix in two steps. First we perform a reduction of the given matrix into Hessenberg form, next we compute the eigenvalues of this resulting Hessenberg matrix via an implicit QR-algorithm. Along the way, we explain how the knowledge of a certain "shift" correction term to the structure can be used to speed up the QR-algorithm for unitary Hessenberg matrices, and how this observation was implicitly used in a paper due to William B.~Gragg. We also treat an analogue of this observation in the Hermitian tridiagonal case.
report.pdf (506K) / mailto: S. Delvaux