Abstract: We present a discussion of three adaptive filtering
algorithms well known for their one-step termination property, in
terms of their relationship with the minimal residual method. These
algorithms are the normalized least mean square (NLMS), Affine
Projection algorithm (APA) and the recursive least squares algorithm
(RLS). The NLMS is shown to be a result of the orthogonality
condition imposed on the instantaneous approximation of the Wiener
equation, while APA and RLS algorithm result from orthogonality
condition in multi-dimensional minimal residual formulation. Further
analysis of the minimal residual formulation for the RLS leads to
a triangular system which also possesses the one-step termination
property (in exact arithmetic)