Fast QR algorithms based on backward prediction errors: A new implementation and its finite precision performance (Q1429409)

The solution of a recursive least-squares (RLS) problem is frequently performed using QR algorithms which are known in different versions. Fast QR algorithms can be subdivided according to the error type (a posteriori vs. a priori) as well as according to the type of the prediction error (forward vs. backward). In this way, four types of fast QR algorithms can be obtained according to this classification. This paper gives a systematic description of those algorithms which are based on the backward prediction errors. For each of the algorithms, two versions are discussed in detail. The computational complexity of the algorithms is compared, and their performance is illustrated using numerical simulations.