Interpolation on the torus using sk-splines with number theoretic knots

For a fixed, continuous, periodic kernel K, an sk-spline is a function of the form sk(x) = c(o) + Sigma(i=1)(n) c(i)K(x - x(i)). In this paper we consider a generalization of the univariate sk-spline to the d-dimensional torus (d greater than or equal to 2), and give almost optimal error estimates of the same order, in power scale, as best trigonometric approximation on Sobolev's classes in L-q. An important component of our method is that the interpolation nodes are generated using number theoretic ideas. (C) 1999 Academic Press.