"Nick" wrote in message <email@example.com>... > I have a large sparse (symmetric positive definite) NxN matrix A, I would like to compute a few select elements of inv(A) without computing the full inverse. > > Obviously we can compute the ith column of inv(A) with the backslash operator which is a much better solution than forming inv(A) explicitly: > ei = zeros(N,1);
I guess you mean e = zeros(N,1);
> e(i) = 1; > ans = A \ e; > > I can extract the jth element of that to get inv(A)(j,i) > > My question is this: can I extract element (i,j) of the inverse without needing to compute the full column i? >
No. Element (i,j) of the inverse matrix is involved in the calculation of all N elements of the j'th column of the identity matrix. Thus the full j'th column of the inverse matrix needs to be determined to extract a single element of this column.
> In matrix notation, I am trying to compute this rapidly: > ej' * inv(A) * ei > (where ej = zeros(N,1); ej(j) = 1;)