Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation

  author = {S.~Knapek},
  title = {Hyperbolic cross approximation of integral operators with
		  smooth kernel},
  journal = {submitted},
  year = {2000},
  annote = {article,256C},
  note = {also as Technical Report 665, SFB 256, Univ.~Bonn},
  abstract = {This paper is concerned with the construction and use of
		  trigonometric approximation spaces for the approximate
		  evaluation of integral operators with smooth kernels. The
		  smoothness classes we consider are mixtures of classes of
		  functions of dominating mixed derivative. We define a scale
		  of nested approximation spaces for the approximation of the
		  kernel that includes the standard full grid spaces as well
		  as the spaces related to hyperbolic cross points. We
		  present theoretical results on the approximation power of
		  these spaces and show under which circumstances these
		  approximation spaces lead to algorithms that break the
		  curse of dimensionality. Blending schemes for these new
		  approximation spaces allow the use of simple data
		  structures and the direct application of fast hierarchical
		  methods such as multilevel methods and fast Fourier
		  transforms. Numerical examples illustrate the theoretical
  ps = { 1}