In this paper, based on the application of the sum-product (SP) algorithm to factor graphs (FGs), we investigate two optimal equalization algorithms, i.e., unconstrained linear equalization and constrained linear equalization for intersymbol interference (ISI) channels, both of which use the criterion of LMMSE. From simulations we know, the MSE performance of these two algorithms is much better than that of the conventional adaptive LMS algorithm based on filters, especially at high SNR However, at low SNR this improvement is less obvious. So an improved algorithm is introduced in order to conquer this deficiency, simulation results show that the proposed algorithm can further achieve a remarkable reduction in MSE at low SNR.