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Alternating Projection Methods

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by René Escalante and Marcos Raydan


2011 / x + 129 pages / Softcover / ISBN: 978-1-611971-93-4 / List Price $62.50 / SIAM Member Price $43.75 / Order Code FA08

Subject Index

Keywords: alternating projection methods, row-action methods, convex feasibility problems, Dykstra's algorithm, acceleration techniques.

This book describes and analyzes all available alternating projection methods for solving the general problem of finding a point in the intersection of several given sets belonging to a Hilbert space. For each method the authors describe and analyze convergence, speed of convergence, acceleration techniques, stopping criteria, and applications. Different types of algorithms and applications are studied for subspaces, linear varieties, and general convex sets. The authors also unify these algorithms into a common theoretical framework.

Alternating Projection Methods provides readers with

  • the theoretical and practical aspects of the most relevant alternating projection methods in a single accessible source;
  • several acceleration techniques for every method it presents and analyzes, including schemes that cannot be found in other books; 
  • full descriptions of several important mathematical problems and specific applications for which the alternating projection methods represent an efficient option; and examples and problems that illustrate this material.

This book can be used as a textbook for advanced undergraduate or first-year graduate students. Because it is comprehensive, it can also be used as a tutorial or a reference by mathematicians and nonmathematicians from many fields of application who need to solve alternating projection problems in their work.

About the Authors
René Escalante is a professor in the Department of Scientific Computing and Statistics and Center for Research (CESMa) at Universidad Simón Bolívar, Venezuela. He served on the faculty of the Scientific Computing Research Center (CCCT) at Universidad Central de Venezuela until 2003. He has published several books and numerous journal articles in scientific computing and mathematical modeling and is currently the Editor-in-Chief of the Bulletin of Computational Applied Mathematics.

Marcos Raydan is a professor in the Department of Scientific Computing and Statistics at Universidad Simón Bolívar and the Scientific Computing Research Center (CCCT) at Universidad Central de Venezuela. He is a member of the editorial board of Computational and Applied Mathematics and the author of over 60 papers on numerical mathematics and scientific computing.

ISBN: 9781611971934

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