Multiplicative perturbation bounds for weighted polar decomposition

In this paper, we obtain the multiplicative perturbation bounds for generalized nonnegative polar factor of weighted polar decomposition under the weighted unitarily invariant norm, weighed Frobenius norm and weighted spectral norm, respectively. More sharper bounds than the known ones are also obtained under certain condition. Moreover, new multiplicative perturbation bounds for weighted unitary polar factor are also given under the weighted unitarily invariant norm, which improve the existing multiplicative perturbation bounds.