key problem in computational linear algebra.  The idea is that you
% first factorize a matrix.  Next, make a low-rank change to A, and patch
% up (or down...) the factorization so that it becomes the factorization of
% the new matrix.  In MATLAB, this only works for dense symmetric positive
% definite matrices, via cholupdate.  This is much faster than computing
% the new factorization from scratch.

n = 1000 ;
A = rand (n) ;
A = A*A' + n*eye (n) ;
w = rand (n,1) ; t = rand (n,1) ; b = rand (n,1) ;
F = fact