data interpolation; smooth interpolation; polyharmonic spline; radial basis function; Fourier transform
We study the problem of construction of the smooth interpolation formula presented as the minimizer of suitable functionals subject to interpolation constraints. We present a procedure for determining the interpolation formula that in a natural way leads to a linear combination of polyharmonic splines complemented with lower order polynomial terms. In general, such formulae can be very useful e.g.\ in geographic information systems or computer aided geometric design. A simple computational example is presented.