The Rate of Convergence in the Method of Alternating Projections

نویسندگان

  • CATALIN BADEA
  • VLADIMIR MÜLLER
چکیده

A generalization of the cosine of the Friedrichs angle between two subspaces to several closed subspaces in a Hilbert space is given. This is used to analyze the rate of convergence in the von Neumann-Halperin method of cyclic alternating projections. General dichotomy theorems are proved, in the Hilbert or Banach space situation, providing conditions under which the alternative QUC/ASC (quick uniform convergence versus arbitrarily slow convergence) holds. Several meanings for ASC are proposed.

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تاریخ انتشار 2010