# Cholesky decomposition of $A+kI$ given Cholesky decomposition of A

Suppose I have the Cholesky decomposition for a symmetric matrix $A$:

$$A = L L^T$$

I wish to compute the Cholesky decomposition for $A+kI$ where $I$ is the identity and $k$ is a scalar. Is there a way to obtain this using the decomposition for $A$ faster than recomputing the Cholesky decomposition from scratch?

-
Have updated the question. If $k$ is negative then $A+kI$ may or may not be positive definite. For an example that is positive definite, take $A=2I$ and $k=-1$. –  Alex Flint Jul 16 '13 at 19:45