It is likely that you have encountered a common problem with the Gaussian

model, a simple fix is to include a small nugget term.

Assuming you are using ordinary kriging the coefficient matrix is in

general not positive definite but still invertible if a valid variogram is

used. The problem is the zero in the last row/last column.

However the problem with the Gaussian is a further complication. If you

examine the graph of a Gaussian you see that it has values that are almost

zero (assuming no nugget) for a considerable distance (relative to the

range) hence when one uses the usual kind of a search neighborhood, i.e.,

only the nearest data locations, this can result in lot of variogram values

in the kriging matrix that are nearly zero. This likely results in an

ill-conditionned matrix and depending on how they attempt to solve the

system of equations it may not have a unique solution.

If the kriging system is written in terms of covariances rather than

variograms then the same kind of a problem occurs but rather than a lot of

values that are close to zero, the values are all close to the sill value.

If you are using simple kriging (as opposed to ordinary) then the same

problem can still occur with a Gaussian model although theoretically the

kriging matrix is postive definite.

I haven't looked to see which equation solver they are using in S+ and it

may be their choice is unusually sensitive to ill-conditionned matrices.

Donald E. Myers

Department of Mathematics

University of Arizona

Tucson, AZ 85721

(520) 621-6859

myers@...
http://www.u.arizona.edu/~donaldm
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