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Chapter 10: Closest Points and Approximation

Chapter 10: Closest Points and Approximation

pp. 126-136

Authors

, University of Warwick
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Summary

We consider the existence of closest points in convex subsets of Hilbert sapces. In particular this enables us to define the orthogonal projection onto a closed linear subspace U of a Hilbert space H, and thereby decompose any element x of H as x=u+v, where u is an element of U and v is contained in its orthogonal complement. We also discuss ‘best approximations’ of elements of H in spaces spanned by collections of elements of H.

Keywords

  • closest points
  • orthogonal projection
  • orthogonal complement
  • best approximations

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