Lecture Notes in Mathematics

Iterative Methods for Fixed Point Problems in Hilbert Spaces

Authors: Cegielski, Andrzej

  • The projection methods for fixed point problems are presented in a consolidated way
  • Over 60 figures help to understand the properties of important classes of algorithmic operators
  • The convergence properties of projection methods follow from a few general convergence theorems presented in the monograph
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About this book

Iterative methods for finding fixed points of non-expansive operators in Hilbert spaces have been described in many publications. In this monograph we try to present the methods in a consolidated way. We introduce several classes of operators, examine their properties, define iterative methods generated by operators from these classes and present general convergence theorems. On this basis we discuss the conditions under which particular methods converge. A large part of the results presented in this monograph can be found in various forms in the literature (although several results presented here are new). We have tried, however, to show that the convergence of a large class of iteration methods follows from general properties of some classes of operators and from some general convergence theorems.

Reviews

From the reviews:

“Cegielski provides us with a very carefully written monograph on solving convex feasibility (and more general fixed point) problems. … Cegielski’s monograph can serve as an excellent source for an upper-level undergraduate or graduate course. … researchers in this area now have a valuable source of recent results on projection methods to which the author contributed considerably in his work over the past two decades. In summary, I highly recommend this book to anyone interested in projection methods, their generalizations and recent developments.” (Heinz H. Bauschke, Mathematical Reviews, July, 2013)

“This book is mainly concerned with iterative methods to obtain fixed points. … this book is an excellent introduction to various aspects of the iterative approximation of fixed points of nonexpansive operators in Hilbert spaces, with focus on their important applications to convex optimization problems. It would be an excellent text for graduate students, and, by the way the material is structured and presented, it will also serve as a useful introductory text for young researchers in this field.” (Vasile Berinde, Zentralblatt MATH, Vol. 1256, 2013)

Table of contents (5 chapters)

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-642-30901-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.95
price for USA
  • ISBN 978-3-642-30900-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Iterative Methods for Fixed Point Problems in Hilbert Spaces
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2057
Copyright
2013
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-30901-4
DOI
10.1007/978-3-642-30901-4
Softcover ISBN
978-3-642-30900-7
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XVI, 298
Number of Illustrations and Tables
58 b/w illustrations, 3 illustrations in colour
Topics