The concepts of backwards consistency and minimality are shown to be the essential tools in studying error propagation in fast least-squares adaptive filters. A conceptual framework identifying the principal error propagation mechanism is developed, allowing the numerical stability of new or existing algorithms to be ascertained without the technical labor previously thought necessary. Order recursive algorithms are confirmed to have intrinsic advantages over their transversal counterparts.
Phillip A. Regalia,
"Numerical stability issues in fast least-squares adaptive algorithms", Proc. SPIE 1565, Adaptive Signal Processing, (1 December 1991); doi: 10.1117/12.49760; https://doi.org/10.1117/12.49760