Rates of convex approximation in non-hilbert spaces

@article{Donahue1997RatesOC,
  title={Rates of convex approximation in non-hilbert spaces},
  author={Michael J. Donahue and Christian Darken and Leonid Gurvits and Eduardo D. Sontag},
  journal={Constructive Approximation},
  year={1997},
  volume={13},
  pages={187-220}
}
This paper deals with sparse approximations by means of convex combinations of elements from a predetermined “basis” subsetS of a function space. Specifically, the focus is on therate at which the lowest achievable error can be reduced as larger subsets ofS are allowed when constructing an approximant. The new results extend those given for Hilbert spaces by Jones and Barron, including, in particular, a computationally attractive incremental approximation scheme. Bounds are derived for broad… CONTINUE READING
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