Date: Nov 13, 2012 2:18 AM
Author: NIcholas
Subject: finding specific elements of inverse matrix

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);
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?

In matrix notation, I am trying to compute this rapidly:
ej' * inv(A) * ei
(where ej = zeros(N,1); ej(j) = 1;)