A Dual Approach to Constrained Interpolationfrom a Convex Subset of Hilbert Space

@article{Deutsch1997ADA,
  title={A Dual Approach to Constrained Interpolationfrom a Convex Subset of Hilbert Space},
  author={Frank Deutsch and Wu Li and Joseph D. Ward},
  journal={Journal of Approximation Theory},
  year={1997},
  volume={90},
  pages={385-414}
}
Many interesting and important problems of best approximationare included in (or can be reduced to) one of the followingtype: in a Hilbert spaceX, find the best approximationPK(x) to anyx?Xfrom the setK?C?A?1(b),whereCis a closed convex subset ofX,Ais a bounded linearoperator fromXinto a finite-dimensional Hilbert spaceY, andb?Y. The main point of this paper is to show thatPK(x)isidenticaltoPC(x+A*y)?the best approximationto a certain perturbationx+A*yofx?from the convexsetCor from a certain… 
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