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Is it possible to compute individual elements of a matrix inverse?

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I have a large sparse regular matrix. Instead of computing the full inverse of it, I just want to determine individual elements of it (mainly the diagonal elements of the inverse). Is there any way to do that in Matlab?
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Stephen23 on 21 Jun 2017
Edited: Stephen23 on 21 Jun 2017
Some light reading to get you started: "Computing the diagonal of the inverse of a sparse matrix" "A Probing Method for Computing the Diagonal of the Matrix Inverse" "FAST ALGORITHM FOR EXTRACTING THE DIAGONAL OF THE INVERSE MATRIX WITH APPLICATION TO THE ELECTRONIC STRUCTURE ANALYSIS OF METALLIC SYSTEMS"
Question: how big is the matrix?

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