Editing Levinson recursion (section)

=== Introductory steps ===
The algorithm proceeds in two steps. In the first step, two sets of vectors, called the ''forward'' and ''backward'' vectors, are established. The forward vectors are used to help get the set of backward vectors; then they can be immediately discarded. The backwards vectors are necessary for the second step, where they are used to build the solution desired.

Levinson–Durbin recursion defines the ''n''<sup>th</sup> "forward vector", denoted <math>\vec f^n</math>, as the vector of length ''n'' which satisfies:

:<math>\mathbf T^n \vec f^n = \hat e_1.</math>

The ''n''<sup>th</sup> "backward vector" <math>\vec b^n</math> is defined similarly; it is the vector of length ''n'' which satisfies:

:<math>\mathbf T^n \vec b^n = \hat e_n.</math>

An important simplification can occur when '''''M''''' is a [[symmetric matrix]]; then the two vectors are related by ''b''<sup>''n''</sup><sub>''i''</sub> = ''f''<sup>''n''</sup><sub>''n''+1−''i''</sub>—that is, they are row-reversals of each other. This can save some extra computation in that special case.