Alternating Projection Methods
Seiten
2011
Society for Industrial & Applied Mathematics,U.S. (Verlag)
978-1-61197-193-4 (ISBN)
Society for Industrial & Applied Mathematics,U.S. (Verlag)
978-1-61197-193-4 (ISBN)
This comprehensive textbook describes and analyzes all available alternating projection methods for solving the general problem of finding a point in the intersection of several given sets that belong to a Hilbert space. It can be used as a textbook for graduate or advanced undergraduate students.
This comprehensive textbook describes and analyzes all available alternating projection methods for solving the general problem of finding a point in the intersection of several given sets that belong to a Hilbert space. For each method, the authors describe and analyze the issues of 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 in a common theoretical framework. Many examples and problems are included in order to reinforce student learning. This book can be used as a textbook for graduate or advanced undergraduate students. Because it is comprehensive, it can also be used as a tutorial or a reference by mathematicians and non-mathematicians from many fields of applications who need to solve alternating projection problems in their work.
This comprehensive textbook describes and analyzes all available alternating projection methods for solving the general problem of finding a point in the intersection of several given sets that belong to a Hilbert space. For each method, the authors describe and analyze the issues of 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 in a common theoretical framework. Many examples and problems are included in order to reinforce student learning. This book can be used as a textbook for graduate or advanced undergraduate students. Because it is comprehensive, it can also be used as a tutorial or a reference by mathematicians and non-mathematicians from many fields of applications who need to solve alternating projection problems in their work.
René Escalante is a professor in the Department of Scientific Computing and Statistics and Center for Research CESMa at Universidad Simón Bolívar, Venezuela. Marcos Raydan is a professor in the Department of Scientific Computing and Statistics at Universidad Simón Bolívar, and also in the Scientific Computing Research Center (CCCT) at Universidad Central de Venezuela.
Preface; 1. Introduction; 2. Overview on spaces; 3. The MAP on subspaces; 4. Row-action methods; 5. Projecting on convex sets; 6. Applications of MAP for matrix problems; Bibliography; Author index; Subject index.
| Reihe/Serie | Fundamentals of Algorithms |
|---|---|
| Verlagsort | New York |
| Sprache | englisch |
| Maße | 177 x 255 mm |
| Gewicht | 250 g |
| Themenwelt | Informatik ► Theorie / Studium ► Algorithmen |
| Mathematik / Informatik ► Mathematik ► Algebra | |
| ISBN-10 | 1-61197-193-4 / 1611971934 |
| ISBN-13 | 978-1-61197-193-4 / 9781611971934 |
| Zustand | Neuware |
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