  In this paper, we investigate the weighted core-EP inverse introduced by
Ferreyra, Levis and Thome. Several computational representations of the
weighted core-EP inverse are obtained in terms of singular-value decomposition,
full-rank decomposition and QR decomposition. These representations are
expressed in terms of various matrix powers as well as matrix product involving
the core-EP inverse, Moore-Penrose inverse and usual matrix inverse. Finally,
those representations involving only Moore-Penrose inverse are compared and
analyzed via computational complexity and numerical examples.
