Acoustic echo cancellation (AEC) is a well-known application of adaptive filters in communication acoustics. To implement AEC for multichannel reproduction systems, powerful adaptation algorithms like the generalized frequency-domain adaptive filtering (GFDAF) algorithm are required for satisfactory convergence behavior. In this paper, the GFDAF algorithm is rigorously derived as an approximation of the block recursive least-squares (RLS) algorithm. Thereby, the original formulation of the GFDAF algorithm is generalized while avoiding an error that has been in the original derivation. The presented algorithm formulation is applied to pruned transform-domain loudspeaker-enclosure-microphone models in a mathematically consistent manner. Such pruned models have recently been proposed to cope with the tremendous computational demands of massive multichannel AEC. Beyond its generalization, a regularization of the GFDAF is shown to have a close relation to the well-known block least-mean-squares algorithm.