Smoothing and interpolation by kriging and with splines

Abstract

Let scalar measurements at distinct points x1, ⋯, xnbe y1, ⋯, yn. We may look for a smooth function f(x)that goes through or near the points (xi, yi). Kriging assumes f(x)is a random function with known (possibly estimable) covariance function (in the simplest case). Splines assume a definition of the smoothness of a nonrandom function f(x). An elementary explanation is given of the fact that spline approximations are special cases of the solution of a kriging problem. © 1984 Plenum Publishing Corporation.