Equivalence between RLS algorithms and the ridge regression technique

Recursive implementations of the least squares algorithm start the computation with a known set of initial conditions. The information contained in new data samples is then used to update the old estimates. Therefore the initialization procedure is seen to be an integral part of recursive algorithms. A number of methods for initializing recursive least squares (RLS) algorithms have been proposed in the literature. The two most common methods are the fast exact initialization and the soft constrained initialization. This paper discusses the equivalence relationship between RLS algorithms that use soft constrained initialization and a widely used technique in statistics called "ridge regression".