Cholesky Decomposition - Updating The Decomposition

Updating The Decomposition

A task that often arises in practice is that one needs to update a Cholesky decomposition. In more details, one has already computed the Cholesky decomposition A = LL* of some matrix A, then one changes the matrix A in some way into another matrix, say, and one wants to compute the Cholesky decomposition of the updated matrix: . The question is now whether one can use the Cholesky decomposition of A that was computed before to compute the Cholesky decomposition of .