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This paper discusses the convergence rates of partial update normalized least mean square (NLMS) algorithms for long, finite impulse response (FIR) adaptive filters. We specify the general form of convergence of tap weight vector's mean deviation for white Guassian input, and analyze several best known partial update algorithms' performance. These results are compared with the conventional NLMS algorithm. We further discuss the similarity in update effects of some partial update algorithms and proportionate-type NLMS algorithms. This theoretically demonstrates that for sparse impulse response system identification with white Guassian input, properly designed partial update NLMS algorithms, although need only a fraction of the fully updated NLMS algorithm's computational power, have the potential of achieving better performance than conventional NLMS.