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[Lapack] Moment matrix eigenvector update

Rank one perturbation of a symmetric matrix:

And the secular equation can be solved
with laed4(N,I,D,Z,rho,Delta,Dlambda,info), Delta is useful for the
calculation of the new eigenvectors. Z is not the original modifying vector
but its transformation with the original eigenvectors.


2006/11/15, Laszlo Sragner <sragner@Domain.Removed>:


if X is an N x M (N>>M) matrix let C = X' * X and C = VDV'

if w is a Mx1 vector what is the diagonalization of ( C + ww' )?

I understand that the trick is to diagonalize (D+pp') where p=Vw
and that this is the heart of the divide and conquer algorithm
but are there any LAPACK function to do it?

I am also interested to do an SVD on
[ X ]
[ -- ]
[ w']

which is an analogous problem and interesting if C is rank defficient.



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