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TW 460
Steven Delvaux and Marc Van Barel
A Hessenberg reduction algorithm for rank structured matrices
Abstract
In this paper we show how to perform the Hessenberg reduction of a rank structured matrix under unitary similarity operations in an efficient way, using the Givens-weight representation which we introduced in an earlier paper. This reduction can be used as a first step for eigenvalue computation. We also show how the algorithm can be modified to compute the bidiagonal reduction of a rank structured matrix, the latter being a preprocessing step for computing the singular values of the matrix. Numerical experiments demonstrate the stability of this approach.
report.pdf (730K) / mailto: M. Van Barel