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sparseinv: sparse inverse subset

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sparseinv: sparse inverse subset

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28 Nov 2011 (Updated )

Computes a subset of inv(A) for a real sparse matrix A, using Takahashi's equations.

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Description

inv(A) is often abused by MATLAB users, but there are times when you need to compute selected entries of inv(A).

The sparseinv function computes the sparse inverse subset of a sparse matrix A. These entries in the inverse subset correspond to nonzero entries in the factorization of A. They can be computed without computing all of the entries in inv(A), so this method is much faster and takes much less memory than inv(A). If A is symmetric and positive definite, then all entries of the diagonal of inv(A) are computed (as well as many off-diagonal terms). This version is restricted to real sparse matrices. A complex version is left for future work.

Example (err will be small):

    load west0479
    A = west0479 ;
    [Z, Zpattern] = sparseinv (A) ;
    S = inv (A) ;
    err = norm (Zpattern .* (Z - S), 1) / norm (S, 1)

Required Products MATLAB
MATLAB release MATLAB 7.13 (R2011b)
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Comments and Ratings (1)
10 Jan 2014 Gabriel Agamennoni

Great submission! It's (almost) exactly what I was looking for. Is there a way to perform low-rank updates of the inverse subset (e.g. like cholupdate)?

Updates
09 Jul 2013

minor fix to sparseinv.m for sparse symmetric positive definite matrices.

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