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Inverse of a sparse matrix could be dense, but what if I'm only interested in the main diagonal of the result? Is there a method that is more efficient than computing the full inverse?

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You may be interested in work of Jok M. Tang and Yousef Saad. Their recent paper "Domain-decomposition-type methods for computing the diagonal of a matrix inverse" has the following abstract:

alt text

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  • $\begingroup$ The slides PEV linked to are by Saad, so there is some redundancy in our answers. $\endgroup$ – Jonas Meyer Jan 22 '11 at 3:35
  • $\begingroup$ I was hoping for something that I could quickly implement using standard linear algebra routines, I guess it's not possible $\endgroup$ – Yaroslav Bulatov Jan 23 '11 at 2:23
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This(explanation of how to find diagonal of an inverse of a sparse matrix) should help.

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We recently implemented in our solver PARDISO such as option where you can these results. The software is available at www.pardiso-project.org.

It is not yet documented in the manual b

Regards, Olaf

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