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In many applications of adaptive data equalization, rapid initial convergence of the adaptive equalizer is of paramount importance. Apparently, the fastest known equalizer adaptation algorithm is based on a recursive least squares estimation algorithm. In this paper we show how the least squares lattice algorithms, recently introduced by Morf and Lee, can be adapted to the equalizer adjustment algorithm. The resulting algorithm, although computationally more complex than certain other equalizer algorithms (including the fast Kalman algorithm), has a number of desirable features which should prove useful in many applications.