Title page for etd-0216111-213732


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URN etd-0216111-213732
Author Wei-Shiou Huang
Author's Email Address No Public.
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Department Applied Mathematics
Year 2010
Semester 2
Degree Master
Type of Document
Language English
Title Convergence Analysis for Inertial Krasnoselskii-Mann Type Iterative Algorithms
Date of Defense 2010-06-17
Page Count 32
Keyword
  • demiclosedness principle
  • KM Type iterative algorithms
  • inertial iteration
  • fixed point
  • Weak convergence
  • nonexpansive mapping
  • Abstract We consider the problem of finding a common fixed point of an infinite family ${T_n}$
    of nonlinear self-mappings of a closed convex subset $C$ of a real Hilbert space $H$. Namely,
    we want to find a point $x$ with the property (assuming such common fixed points exist):
     [
       xin igcap_{n=1}^infty ext{Fix}(T_n).
     ]
    We will use the Krasnoselskii-Mann (KM) Type inertial iterative algorithms of the form
    $$ x_{n+1} = ((1-alpha_n)I+alpha_nT_n)y_n,quad
               y_n = x_n + eta_n(x_n-x_{n-1}).eqno(*)$$
    We discuss the convergence properties of the sequence ${x_n}$ generated by this algorithm (*).
    In particular, we prove that ${x_n}$ converges weakly to a common fixed point of the family
    ${T_n}$ under certain conditions imposed on the sequences ${alpha_n}$ and ${eta_n}$.
    Advisory Committee
  • Lai-Jiu Lin - chair
  • Jen-Chih Yao - co-chair
  • Ngai-Ching Wong - co-chair
  • Hong-Kun Xu - advisor
  • Files
  • etd-0216111-213732.pdf
  • indicate access worldwide
    Date of Submission 2011-02-16

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