This paper describes a novel efficient algorithm appropriate for adapting f
ilters of long order. The scheme is an exact block processing counterpart o
f the recently introduced fast Newton transversal filtering algorithm, The
filters required by the algorithm blocks are much smaller than the filter l
ength, and the obtained estimates are mathematically equivalent to those of
the sample-by-sample version. This leads to a substantial saving in comput
ational complexity without sacrificing performance as well as not having to
resort to long processing delays, which limit the performance of the adapt
ive system.