This paper presents a fast technique for fitting a Kriging surface of the form s(·) = ∑j𝛼jΦ (·-xj)+ ∑ᵐj=1 ⋎jqj(·), where <Φ is a semi-variogram determined from the data. Finding the coefficients of s by conventional techniques requires 𝒪 (N³) operations, and 𝒪 (N²) storage. Numerical evidence suggests that for typical <Φ's the iterative method presented here requires 𝒪 (N log N) operations and 𝒪(N) storage.