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 t he form sk(x) = c(o) + Sigma(i=1)(n) c(i)K(x - x(i)). In this paper we cons ider a generalization of the univariate sk-spline to the d-dimensional toru s (d greater than or equal to 2), and give almost optimal error estimates o f the same order, in power scale, as best trigonometric approximation on So bolev's classes in L-q. An important component of our method is that the in terpolation nodes are generated using number theoretic ideas. (C) 1999 Acad emic Press.