In the article we propose methods of the mean-square optimal linear interpolation of the functional which depend on the unknown values of the multidimensional stationary random field based on observed data of the field with noise. Under condition of spectral certainty when the spectral densities of the stationary fields are known we derive formulas for calculating the spectral characteristics and the mean-square errors of the estimates of the functional. Analogous results are derived for the case of observations of the field without noise. In the case of spectral uncertainty when certain sets of admissible densities are given we derive the relations that the least spectral densities satisfy.

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