Re: Updating Eigenvectors
- From: Carl Christian Kjelgaard Mikkelsen <cmikkels@xxxxxxxxxxxxx>
- Date: Mon, 11 Aug 2008 12:39:36 -0400
Behjat wrote:
Hi,
I am looking for efficient methods of updating the eigenvectors when
the dimensions of the matrix is incremented.
Specifically, if I have a solution to the generalized eigenvalue
problem Ax = B $\lambda$ x with A and B of dimensions nxn. Now A and
B are updated to A' and B' of dimensions (n+1)x(n+1) by appending a
row, column and a diagonal element. Are there any efficient ways of
solving for A'x' = B' $\lambda'$ x'?
Thanks,
Behjat
Extend your known matrices A, B and your vector x trivially, by setting
A(n+1,n+1)=\lambda, B(n+1,n+1)=1, and, x(n+1)=1. Then treat A', B' as rank 1 perturbations of your extended A, B.
I can not point you to the right algorithm, as it is a bit outside my field, but googling "low rank perturbation +eigenvalue problem", looks promising.
Ah, I see Spellucci has already answered this question
http://www.math.niu.edu/~rusin/known-math/01_incoming/SVD_update
/CCKM
.
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