Prof Brian Ripley <[EMAIL PROTECTED]> writes:
> On Thu, 16 Jun 2005, Joshua Gilbert wrote:
>
> > I need to compute generalized eigenvalues. The eigen function in base
> > doesn't do it and I can't find a package that does.
>
> They are very rarely used in statistics, so this is not surprising.
An aside, going a bit off-topic:
However, there's the related generalized singular value decomposition:
K = U Sigma inv(T)
L = V M inv(T)
U'U = V'V = I ; Sigma and M diagonal (Sigma^2 + M^2 = I by
convention) ; T regular
(Look at K'K and L'L to see the connection.)
This is used in Tikhonov regularization, which is penalized least
squares, which is a statistical issue (whether numerical analysts
realize it or not). Smoothing splines is a special case. Deconvolution
is another.
> I presume you mean solving Ax = lambda B x: if B is non-singular this
> reduces to a conventional eigenproblem for B^{-1}A.
(There are some complications if both A and B are singular. That's
why the GSVD has that peculiar-looking convention.)
--
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c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K
(*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918
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