Some new perturbation bounds for both weighted unitary polar factors and generalized nonnegative polar factors of the weighted polar decompositions are presented without the restriction that and its perturbed matrix have the same rank. These bounds improve the corresponding recent results.
Pingping Zhang. Hu Yang. Hanyu Li. "Relative and Absolute Perturbation Bounds for Weighted Polar Decomposition." J. Appl. Math. 2012 1 - 15, 2012. https://doi.org/10.1155/2012/219025