However broad the Decomposition-based Zero-forcing (DBZF) precoder
acceptance may be, reducing the computational complexity of its implementation is an
absolute necessity for the VDSL networking professionals. The paper digs deeper into
this problem from the perspective of matrix inversion which is inherent in the very
nature of the DBZF. Five strategies considered here differ in mode of action: three of
them include matrix inversion, and two others drop implementing the procedure. While
the baseline strategy itemized under No. 1 acts with the Gaussian LU-decomposition,
strategy No. 2 deals with the Jordanian LU-decomposition thereby enabling mild
reduction of the operation count. Strategy No. 3 works for more significant reduction as
it operates with the elimination form of the inverse matrix. The most cost-cutting are
strategies excluding the question of matrix inversion and replacing it by far more
straightforward linear system solution, as it is in Strategy No. 4. An alternative
strategy No. 5 uses the least squares-based square-root-type sequential system solution
and it is the most accurate computational procedure when compared with other
strategies
