In the computation of and described in the previous section, the inverse is never actually computed; an equation of the form

is solved for by using a modified Gaussian elimination algorithm that takes advantage of the fact that is symmetric with constant diagonal that is larger than all offdiagonal elements. The SINGULAR= option pertains to this algorithm. The value specified for the SINGULAR= option is scaled by before comparison with the pivot element.
For conditional simulations, the largest matrix held in core memory at any one time depends on the number of grid points and data points. Using the previous notation, the datadata covariance matrix is , where n is the number of nonmissing observations for the VAR= variable in the DATA= data set. The griddata cross covariance is , where k is the number of grid points. The gridgrid covariance is . The maximum memory required at any one time for storing these matrices is

There are additional memory requirements that add to the total memory usage, but usually these matrix calculations dominate, especially when the number of grid points is large.