A tree classification of algorithms for Toeplitz and related equations including generalized Levinson and doubling type algoritms

A survey of several methods for matrix inversion currently used in linear estimation is presented. The algorithms considered belong to two classes: order recursive and function recursive. For each class a tree representation of the performed operations helps in classifying the various algorithms. Novel stochastic derivations and interpretations of the update equations are introduced that provide new insights into the structure of these procedures.