Updating Eigenvectors

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
.

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