We know that LU decomposition is an important method for stochastic simulation of 2D RF. Assume the covariance matrix of regionalized RVs is C, it can be decomposed as C=LU according to the LU algorithm, then a RF can be generated by X=L'*y, where y is a vector consisting of independent standard normal random numbers. I want to know whether can I use LU decomposition for simulation if n observations exist as the conditioning data? If so, how can it be demonstrated?