This study deals with an adaptive strategy for the equalization of pulse-amplitude-modulated signals in the presence of intersymbol interference and additive note. The successive overrelaxation iterative technique is used as the algorithm for the iterative adjustment of the equalizer coefficients during a training period for the minimization of the mean square error. With 2-cyclic and non-negative Jacobi matrices substantial improvement was demonstrated in the rate of convergence over the commonly used gradient techniques. The Jacobi theorems were also extended to non-positive Jacobi matrices. Numerical examples strongly indicate that the improvements obtained for the special cases are possible for general channel characteristics. The technique was analytically demonstrated to decrease the mean square error (norm) at each iteration for a large range of parameter values for light or moderate intersymbol interference and for small intervals for general channels. Again, numerical examples indicate that the norm-decreasing property is valid for a much larger parameter range for all types of intersymbol interference. Analytically, convergence of the relaxation algorithm was proven in a noisy environment and the coefficient variance was demonstrated to be bounded. Numerical simulations conducted indicate that the relaxation algorithm consistently converged much faster than the gradient techniques; hence, it requires much less time in the training period than do the gradients.