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

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

Answer 1

[Steven Lord]

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.