The numerical properties of the recursive least squares (RLS) algorithm and its fast versions have been extensively studied. However, very few investigations are reported concerning the numerical behavior of the predictor based least squares (PLS) algorithms that provide the same least squares solutions as the RLS algorithm. This paper presents a comparative study on the numerical performances of the RLS and the backward PLS (BPLS) algorithms. Theoretical analysis of three main instability sources reported in the literature, including the over-range of the conversion factor, the loss of symmetry and the loss of positive definiteness of the inverse correlation matrix, has been done under a finite-precision arithmetic. Simulation results have confirmed the validity of our analysis. The results show that three main instability sources encountered in the RLS algorithm do not exist in the BPLS algorithm. Consequently, the BPLS algorithm provides a much more stable and robust numerical performance compared with the RLS algorithm.
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