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finding specific elements of inverse matrix
Posted:
Nov 13, 2012 2:18 AM


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;)



