🚀 go-pugleaf

I am interested in an efficient routine to compute the determinant of a matrix
of size n (n < 100), when only one of the terms of the determinant has been 
changed; in terms of the determinant of the original matrix.

To make it more clear,

Step 1: I have this matrix G and i need to compute its determinant
once. (this is quite easy since there are canned routines for this)

Step 2: But then i just change only of its elements and compute its
determinant.
(Let G' be the new matrix)

Step 2 is repeated quite a few times and each time G' differs from G at
just a single
element. So does any of you know about any public domain routine which could
perform step 2 more efficiently than just by computing the determinant? (like
finding the determinant of G' in terms of determinant of G and the
changed element).

I looked into different techniques of evaluating the determinant. One
method was
to expand the determinant into a sum of n! terms and just grouping the
(n-1)! terms corresponding to the changed term. But my feeling was this would
be more time consuming than computing the determinant itself (which is of
order n**3 if LU factorisation is used). Correct me if i am wrong and 
is there any simpler technique to compute the determinant in such a case?

Thanks

Anand