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9781611971934 Academic Inspection Copy

Alternating Projection Methods

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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 is a comprehensive and accessible source of information, providing readers with the theoretical and practical aspects of the most relevant alternating projection methods. It features several acceleration techniques for every method it presents and analyzes, including schemes that cannot be found in other books. It also provides full descriptions of several important mathematical problems and specific applications for which the alternating projection methods represent an efficient option. Examples and problems that illustrate this material are also included.
Rene Escalante is a professor in the Department of Scientific Computing and Statistics and Center for Research CESMa at Universidad Simon Bolivar, Venezuela. Marcos Raydan is a professor in the Department of Scientific Computing and Statistics at Universidad Simon Bolivar, and also in the Scientific Computing Research Center (CCCT) at Universidad Central de Venezuela.
Preface Chapter 1: Introduction Chapter 2: Overview on Spaces Chapter 3: The MAP on Subspaces Chapter 4: Row-Action Methods Chapter 5: Projecting on Convex Sets Chapter 6: Applications of MAP for Matrix Problems Bibliography Author Index Subject Index.
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