AP-Algorithm
The fastest known Gradient Algorithm for acoustic-echo-cancellation, which takes the [see page 17, same form] as the NLMS-algorithm except it uses Vector error instead of scalar and a Matrix signal, not a vector signal. Note: At a high level you can conclude AP Converges faster than LMS because it searches in more dimensions.
If the number of dimensions used by AP is 1, then AP is exactly equivalent to NLMS.