Relative perturbation bounds for weighted polar decomposition

In this paper, we obtain the relative perturbation bounds for weighted unitary polar factors of the weighted polar decomposition in the weighted unitarily invariant norm, the weighted spectral norm, and the weighted Frobenius norm. As special cases, we also derive the new bounds for subunitary and unitary polar factors of (generalized) polar decomposition. These special bounds improve the corresponding results published recently to some extent.