When using ordinary Kriging, I need to solving linear equations to calculate the weights.
At the Lagrange multiplier step, sometimes the semivariogram matrix is singular and cannot be calculated the inverse matrix.
Does anyone know why the semivariogram matrix becomes a singular matrix? Or how to avoid this situation?
In general, when you are trying to use the matrix method to solve linear equations and you end up with a singular matrix is when you don't have enough equations. Singular matrix basically tells you that you have multiple copies of the same equation.
For example, if you want to solve 3 variable problem with 3 equations, but 2 of the equations are x+y-z=0 and 2x+2y-2z=0, then you'll have a singular matrix. Just make sure you have enough points to apply the interpolation.
The degree of freedom (number of the equations minus number of the variables) should not be negative. At least, it should be zero and this implies that the number of equations and variables are the same. The more equation you have, the more accurate your estimation would be. Note that each of two distinct equations must be independent to avoid the singular matrices in estimation.
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