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

  author = {M. Hegland and J. Garcke and V. Challis},
  title = {The combination technique and some generalisations},
  journal = {Linear Algebra and its Applications},
  year = {2007},
  volume = {420},
  pages = {249--275},
  number = {2--3},
  abstract = {The combination technique has repeatedly been shown to be
		  an effective tool for the approximation with sparse grid
		  spaces. Little is known about the reasons of this
		  effectiveness and in some cases the combination technique
		  can even break down. It is known, however, that the
		  combination technique produces an exact result in the case
		  of a projection into a sparse grid space if the involved
		  partial projections commute. The performance of the
		  combination technique is analysed using a projection
		  framework and the C/S decomposition. Error bounds are given
		  in terms of angles between the spanning subspaces or the
		  projections onto these subspaces. Based on this analysis
		  modified combination coefficients are derived which are
		  optimal in a certain sense and which can substantially
		  extend the applicability and performance of the combination
		  technique. },
  annote = {journal},
  doi = {doi:10.1016/j.laa.2006.07.014},
  file = {opticomLAA.pdf:http\://},
  pdf = { 1}