I have a problem where I have the Cholesky factorization ($A=LL'$) of a symmetric positive-definite matrix. Now, I need to add a new row and column somewhere in the "middle" of the matrix and compute the factorization again.
I am aware of the answer if the addition was at the last row and column as discussed here.
I was wondering what is the most optimum way to perform this decomposition. Note: It is guaranteed that the matrix will remain SPD even after the addition of the extra row and column. Any help is appreciated. This is my first post on stack exchange, so kindly forgive my mistakes.
Thanks in advance!