To generate a predicted value at a single grid point by using data points, PROC KRIGE2D must solve the following kriging system:

where the dimensions of are , and the right-hand-side has one column.

Holding the matrix and vector associated with this system in core requires approximately bytes. The CPU time used in solving the system is proportional to . For large , this time dominates the O() time to compute the elements of the covariance matrix from the specified covariance or semivariogram model.

For local kriging, the kriging system is set up and solved for each grid point. Part of the setup process involves determining the neighborhood of each grid point. A fast K-D tree algorithm is used to determine neighborhoods. For grid points, the dominant CPU time factor is setting up and solving the kriging systems. The in the algorithm of the section Ordinary Kriging is the number of data points in a given neighborhood, and it can differ for each grid point.

In global kriging, the entire input data set and all grid points are used to set up and solve the single system

Again has dimensions , but and now have columns, where is the number of grid points. Memory requirements are approximately bytes. The CPU time used in solving the system is still dominated by the factorization of the left-hand side.