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A straightforward method is presented for the construction of constrained realizations of Gaussian fields, considering a Gaussian random field and its ensemble mean field, given a set of constraints. The residual of the field from its mean is statistically independent of the actual numerical value of the constraints. The algorithm is based on a simple construction of this residual field, which is then added to the analytically calculated mean field. This algorithm is exact and involves no iterations. The algorithm facilitates the generation of the initial conditions for N-body simulations which obey a few hundreds of constraints imposed by the observable universe.
Hoffman et al. (Tue,) studied this question.