Stability of recursive QRD-LS algorithms using finite-precision systolic array implementation

A proof of the stability (in the sense of bounded input/bounded output) of the recursive QRD-LS algorithm using finite-precision systolic array implementation is presented. Two popular systolic array structures are considered. A similar proof can be extended to other systolic implementations. The first structure discussed is due to W.M. Gentleman and H.T. Kung (1981), and the second one is due to J.G. McWhirter (1983).<>