Alternating Projection Methods (fundamentals Of Algorithms)

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