A unified SQRT-free rank-1 up/down-dating approach for recursive least-squares problems

Planar (Givens) and hyperbolic rotations are the most commonly used methods in performing QRD up/downdating. Since the square-root operation takes up much area and its computational time is slow (due to many iterations), the associated area/time efficiency is poor. This is the first effort to establish the basic understanding toward all known square-root-free QRD algorithms, from which the basic criterion is seen to be simple. This unified approach provides a fundamental framework for the square-root-free RLS algorithms essential for practical VLSI implementations