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How to quickly update the inverse for a sparse matrix when a row changes?

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Benson Gou
Benson Gou on 28 Oct 2020
Answered: Steven Lord on 28 Oct 2020
Dear All,
I have a square very sparse matrix A with a dimension 4000 by 4000, and I have its inverse InvA. Now a row in A changes which is called matrix A1, how can I quickly obtain the inverse of A1 making use of InvA?
Thanks a lot.
Benson

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Answers (1)

Steven Lord
Steven Lord on 28 Oct 2020
You can't even be confident that A1 is invertible.
A = speye(5)
invA = inv(A)
A1 = A;
A1(3, 3) = 0 % changing one element
What is the inverse of A1?
But the Sherman-Morrison formula and the Woodbury matrix identity may be of interest to you.

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