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**Fast residual computation for sliding window recursive least squares methods.**
*(English)*
Zbl 0875.93576

Summary: A new algorithm which directly computes a component of the residual vector without finding the weight (solution) vector is introduced for the recursive least squares (RLS) problem with sliding window method using the QR decomposition. This algorithm uses stabilized hyperbolic rotations for downdating. An algorithm associated with the LINPACK downdating scheme is also presented for comparison. The algorithm based on stabilized hyperbolic rotations is faster than the one based on LINPACK downdating algorithm and achieves at least the same accuracy as the LINPACK algorithm. Moreover, the same systolic array for exponential window method can be used for sliding window method when the downdating is done with stabilized hyperbolic rotations.

### MSC:

93E24 | Least squares and related methods for stochastic control systems |

94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |