If I have a psd, symmetric matrix $\mathbf{A}$ and I need to do LU decomps on $\mathbf{B_i}= \mathbf{A} + \mathbf{D_i}$ (where $\mathbf{D_i}$ is a diagonal psd matrix, where $\mathbf{D_i}$ changes randomly). Is there an easy way to go from the LU of $\mathbf{A}$ + some function of $\mathbf{D_i}$ to get the LU of $\mathbf{B_i}$?
Any references in the literature would be greatly appreciated.