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Topic: finding specific elements of inverse matrix
Replies: 2   Last Post: Nov 13, 2012 3:17 PM

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Torsten

Posts: 1,472
Registered: 11/8/10
Re: finding specific elements of inverse matrix
Posted: Nov 13, 2012 3:02 AM
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"Nick" wrote in message <k7ss7j$h04$1@newscl01ah.mathworks.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;)


Best wishes
Torsten.



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