# Fast Recursive Least-Squares Ladder Algorithms

• Peter Strobach
Part of the Springer Series in Information Sciences book series (SSINF, volume 21)

## Abstract

Chapters 7 and 8 have illuminated the classes of ladder algorithms that are based on a pure order recursive construction of the ladder form. In this type of algorithm, the central problem appeared to be the order recursive updating of the covariance Cm(t) according to
$${{{\text{C}}}_{{\text{m}}}}{\text{(t)}}{\mkern 1mu} {\mkern 1mu} {\text{ = }}{\mkern 1mu} {{{\text{C}}}_{{{\text{m - 1}}}}}{\text{(t)}}{\mkern 1mu} {\text{ + }}{\mkern 1mu} \ldots {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\text{.}}$$
(9.1)
Two solutions to the problem (9.1) have been presented. The first approach, discussed in Chap. 7, was based on the incorporation of transversal predictor parameters as intermediate recursion variables in Levinson-type algorithms. Alternatively, Chap. 8 introduced the algorithms of the PORLA type where the objective was to replace the Levinson-type recursion by inner product recursions, where inner products, also termed “generalized residual energies”, were used as intermediate recursion variables, hence avoiding the explicit computation of transversal predictor parameters.

## Keywords

Reflection Coefficient Projection Operator Residual Energy Residual Vector Differential Covariance
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Chapter 9

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25. 9.25
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26. 9.26
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