How to fast get the SVD of $A-xx^T$ based on the SVD results of $A$?

Question

In the question, $A\in R^{d\times d}$ is a positive semi-definite matrix, $x\in R^{d}$ is a vector, and SVD means Singular Value Decomposition.

This question seems to be related with 'Rank-One Modification of the Symmetric Eigenproblem'. The application of this question includes PCA for uncentered data https://arxiv.org/pdf/1408.5823v5.pdf .