I want to ask a question about invertible matrix. Suppose there is a $n\times n$ symmetric and invertible matrix $M$, and we know its Cholesky decomposion as $M=LL'$. Then do we have an efficient way to calculate $(M+D)^{-1}$, where $D=diag(d\_1,...,d\_n)$ with positive diagonal entries, by taking the information of $M=LL'$ rather than calculating from scratch with $M+D$ directly? Or what if for the sepcial case $D=dI\_n$?

Thanks a lot!