A sparse digital adaptive equalizer including forward and feedback Finite Impulse Response (FIR) filters exhibits improved Least Mean Square operation. A switch assigns one of several multipliers of each filter to any one of the tap locations of that filter. Each multiplier is initially assigned to a preselected tap location with a predetermined weighting coefficient. After completing successive time cycles having a duration equal to a given number of data sample periods, for each filter there is determined (a) a first group of coefficients associated with multipliers then assigned to non-zero value tap locations, and (b) a second group of coefficients associated with multipliers then assigned to zero valued locations. Multipliers associated with first group coefficients during a just-completed time cycle retain their tap locations during the next time cycle. Multipliers associated with second group coefficients during a just-completed time cycle are reassigned to new tap locations for use during the next time cycle.