Editing Cholesky decomposition (section)

==== Rank-one downdate ====
A ''rank-one downdate'' is similar to a rank-one update, except that the addition is replaced by subtraction: <math display=inline> \tilde{\mathbf{A}} = \mathbf{A} - \mathbf{x} \mathbf{x}^* </math>. This only works if the new matrix <math display=inline> \tilde{\mathbf{A}} </math> is still positive definite.

The code for the rank-one update shown above can easily be adapted to do a rank-one downdate: one merely needs to replace the two additions in the assignment to <code>r</code> and <code>L((k+1):n, k)</code> by subtractions.