@Article{borwein2015convergence,
  Title                    = {Convergence rate analysis for averaged fixed point iterations in the presence of {H}\"older regularity},
  Author                   = {Borwein, Jonathan M and Li, Guoyin and Tam, Matthew K},
  Journal                  = {arXiv:1510.06823},
  Year                     = {2015},

  Abstract                 = {In this paper, we establish sublinear and linear convergence of fixed point iterations generated by averaged operators in a Hilbert space. Our results are achieved under a bounded H\"older regularity assumption which generalizes the well-known notion of bounded linear regularity. As an application of our results, we provide a convergence rate analysis for Krasnoselskii--Mann iterations, the cyclic projection algorithm, and the Douglas--Rachford feasibility algorithm along with some variants. In the important case in which the underlying sets are convex sets described by convex polynomials in a finite dimensional space, we show that the H\"older regularity properties are automatically satisfied, from which sublinear convergence follows.},
  Owner                    = {matt},
  Timestamp                = {2015.11.05},
  Url_arxiv                = {http://arxiv.org/abs/1510.06823}
}

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