Single-input Eigenvalue Assignment Algorithms: a Close-look

A close-look is given at the single-input eigenvalue assignment methods. Several previously known backward stable QR algorithms are tied together in a common framework of which each is a special case, and their connection to an explicit expression for the feedback vector is exposed. A simple new algorithm is presented and its backward stability is established by round-oo-error analysis. The diierences between this new algorithm and the other QR algorithms are discussed. Also, the round-oo error analysis of a simple recursive algorithm for the problem (Datta (1987)) is presented. The analysis shows that the latter is reliable, and the reliability can be determined during the execution of the algorithm rather cheaply. Finally, some numerical experiments comparing some of the methods are reported.