New perturbation bounds for the W-weighted Drazin inverse

The constructive perturbation bounds for the W-weighted Drazin inverse are derived by two approaches in this paper. One uses the matrixG = (A+E)W]^l?(AW)^l, whereA, E ∈ C ^mxn ,W ∈ C ^nxm ,l = max Ind(AW), Ind(A + E)W]. The other uses a technique proposed by G. Stewart and based on perturbation theory for invariant subspaces of a matrix. The new approaches to develop perturbation bounds for W-weighted Drazin inverse of a matrix extend the previous results in 19, 29, 31, 36, 42, 44]. Several examples which indicate the sharpness of the new perturbation bounds are presented.