Research Group of Prof. Dr. J. Garcke
Institute for Numerical Simulation

  author = {Jochen Garcke and Markus Hegland},
  title = {Fitting multidimensional data using gradient penalties and
		  combination techniques},
  booktitle = {Proceedings of HPSC 2006, Hanoi, Vietnam},
  year = {2008},
  editor = {Bock, H.G. and Kostina, E. and Hoang, X.P. and Rannacher,
  pages = {235--248},
  abstract = { Sparse grids, combined with gradient penalties provide an
		  attractive tool for regularised least squares fitting. It
		  has earlier been found that the combination technique,
		  which allows the approximation of the sparse grid fit with
		  a linear combination of fits on partial grids, is here not
		  as effective as it is in the case of elliptic partial
		  differential equations. We argue that this is due to the
		  irregular and random data distribution, as well as the
		  proportion of the number of data to the grid resolution.
		  These effects are investigated both in theory and
		  experiments. The application of modified ``optimal''
		  combination coefficients provides an advantage over the
		  ones used originally for the numerical solution of PDEs,
		  who in this case simply amplify the sampling noise. As part
		  of this investigation we also show how overfitting arises
		  when the mesh size goes to zero. },
  annote = {other},
  file = {hanoi.pdf:http\://},
  optpublisher = {Springer},
  pdf = { 1}