> It is well known that when inverting a
> matrix it is much better (for numerical reasons)
> that the higher values
> are on the diagonal and the lower values far off the
> diagonal.
Have you not heard of "pivoting"?
The computational "problems" of using a matrix based
on the semi-variogram rather than the covariance are
removed totally by putting the last equation first in
the matrix. Of course, this means you cannot use a
computational algorithm which demands a symmetric
matrix, but so what?
Alternatively, you pivot on the largest term in the
first equation, then the second etc. I did a lot of
experimentation with this around 15 years ago and
found that the two (covariance and semi-variogram)
sets of equations become identical after around the
second or third 'pivot'.
Please let us not confuse programming problems with
geostatistical problems.
There are a lot of packages out there which ask you to
model the semi-variogram and then use a covariance for
kriging. There are a lot of packages out there which
model the semi-variogram and krige with the
semi-variogram. Are there main stream geostatistical
(as opposed to statistical or strict GIS) packages
which model the covariance?
Isobel Clark
http://geoecosse.bizland.com
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