Diagonal of an inverse of a sparse matrix

Question

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?

score 2 · Accepted Answer · answered Jan 22 '11 at 03:00

2

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:

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answered Jan 22 '11 at 03:00

Jonas Meyer

53,602

The slides PEV linked to are by Saad, so there is some redundancy in our answers. – Jonas Meyer Jan 22 '11 at 03:35
I was hoping for something that I could quickly implement using standard linear algebra routines, I guess it's not possible – Yaroslav Bulatov Jan 23 '11 at 02:23

score 1 · Answer 2 · answered Jan 22 '11 at 02:56

1

This(explanation of how to find diagonal of an inverse of a sparse matrix) should help.

answered Jan 22 '11 at 02:56

NebulousReveal

13,935

score 1 · Answer 3 · answered Nov 27 '12 at 19:59

1

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

answered Nov 27 '12 at 19:59

olaf schenk

21

Diagonal of an inverse of a sparse matrix

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