Adaptive generalized decision feedback equalization (GDFE) allows variations in one or more channels and noise of a multi-line/multi-channel communication system to be tracked. Such tracking can be used in vector upstream (one-sided) situations in communication systems such as ADSL and VDSL, among others. The GDFE may be separated into adaptive and static portions and/or components. Either a feedforward section or a feedback section (or both) can be separated to create a static component and an adaptive component. The adaptive components adjust to the instantaneous channel and noise changes (for example, using the instantaneous errors and simple LMS algorithms). When the channel and noise do not exhibit any time-variation, the adaptive filters can zero themselves. Local updating of adaptive feedforward and/or feedback filters addresses rapid changes to the spatial correlation of noise and/or changes to the multi-line channel (for example, time-variation due to temperature changes, component variations, mechanical stress, and other reasons), without disruption to separate static feedforward and/or feedback filters supplied by a controller, such as a DSL optimizer or the like that can assist by doing the heavier calculations and providing vectoring information and data to the DSL line components. An efficient implementation is provided of any triangularization of the binder channel that characterizes multi-user vectored-DMT DSL. Adaptation also allows correction of any inaccuracy in initially or previously reported crosstalk transfer functions and noise spatial correlation.