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

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Philipp Glira
Philipp Glira on 21 Jun 2017
Edited: Stephen on 21 Jun 2017
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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Stephen
Stephen on 21 Jun 2017
Some light reading to get you started:
http://www-users.cs.umn.edu/~saad/PDF/Sparse_days_06_15_2010.pdf: "Computing the diagonal of the inverse of a sparse matrix"
http://www-users.cs.umn.edu/~saad/PDF/umsi-2010-42.pdf: "A Probing Method for Computing the Diagonal of the Matrix Inverse"
https://web.stanford.edu/~lexing/publication/diagonal.pdf: "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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