Suppose we know the SVD of matrix $\bf A$, and $\bf B$ is a slight perturbation of $A$ (e.g. $\|{\bf B}-{\bf A}\|_{\text F}$ is relatively small), then is there any method that can efficiently compute the SVD of $\bf B$? That is, can the knowledge of SVD of $\bf A$ be helpful for SVD of $\bf B$?

I searched a little bit and found there are some papers on the bound of perturbation, e.g. Perturbation Theory for the Singular Value Decomposition, but I currently have no luck in finding a method to compute SVD of perturbation taking advantage of the SVD of the original matrix.

Any help or reference will be very much appreciated!