[Thread Prev][Thread Next][Index]

Re: [ferret_users] first couple of eofs only using eof_space, eof_tfunc



Hi Billy and Ferret users,

| There is no way to find only some of the eigenvalues. I think that
| is true in theory (please correct me if I am wrong),

This is irrelevant to the present question, but actually, it seems
that eigenvectors associated with largest eigenvalues are
algorithmically easy to obtain.  (In numerical libraries, you often
find subroutines to do that.)  For a positive definite symmetric
matrix A (as the simplest example and it applies to the covariance
matrix for EOF computation), a unit vector v that maximizes (v, A v)
== transpose(v) A v is the eigenvector associated with the largest
eigenvalue.  There seems to be algorithms utilizing such a property as
this, though I'm not familiar with such numerical analysis.  Here is
a (probably simplest) example:

  http://homepage.univie.ac.at/Franz.Vesely/cp0102/dx/node29.html

Anyway, this is irrelevant to the present question.  Even when you
want largest eigenvalues, probably you still need to store the entire
covariance matrix.

Ryo


[Thread Prev][Thread Next][Index]

Contact Us
Dept of Commerce / NOAA / OAR / PMEL / TMAP

Privacy Policy | Disclaimer | Accessibility Statement