Efficiency of different equation solvers in cokriging

Abstract

When the system of equations for cokriging is written in matrix form the sample-sample covariance matrix may be considered either as an mn × mn matrix of scalar entries, where n is the number of sample locations and m is the number of variables, or as an n × n matrix whose entries are m × m matrices. Similarly, the point-sample covariance matrix may be considered as m column vectors or as a single column whose entries are m × m matrices. The formulation in the original program assumed that the submatrix structure should be preserved, but this is not necessary. The scalar matrix formulation allows for the use of a standard Gaussian elimination to reduce the matrix to diagonal form or for reduction to upper triangular form together with back substitution. Both methods result in significant reductions in computing time.