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We consider a multivariate piecewise linear interpolation of a continuousrandom field on a d-dimensional cube. The approximation performance is measuredby the integrated mean square error. Multivariate piecewise linear interpolatoris defined by N field observations on a locations grid (or design). Weinvestigate the class of locally stationary random fields whose local behavioris like a fractional Brownian field in mean square sense and find theasymptotic approximation accuracy for a sequence of designs for large N.Moreover, for certain classes of continuous and continuously differentiablefields we provide the upper bound for the approximation accuracy in the uniformmean square norm.

Multivariate piecewise linear interpolation of a random field