# LU Decomposition of PSD Matrix + Diagonal Matrix

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.