Описание: With the advent of approximation algorithms for NP-hard combinatorial optimization problems, several techniques from exact optimization such as the primal-dual method have proven their staying power and versatility. This book describes a simple and powerful method that is iterative in essence and similarly useful in a variety of settings for exact and approximate optimization. The authors highlight the commonality and uses of this method to prove a variety of classical polyhedral results on matchings, trees, matroids and flows. The presentation style is elementary enough to be accessible to anyone with exposure to basic linear algebra and graph theory, making the book suitable for introductory courses in combinatorial optimization at the upper undergraduate and beginning graduate levels. Discussions of advanced applications illustrate their potential for future application in research in approximation algorithms.
In the second edition of this classic monograph, complete with four new chapters and updated references, readers will now have access to content describing and analysing classical and modern methods with emphasis on the algebraic structure of linear iteration, which is usually ignored in other literature.
The necessary amount of work increases dramatically with the size of systems, so one has to search for algorithms that most efficiently and accurately solve systems of, e.g., several million equations. The choice of algorithms depends on the special properties the matrices in practice have. An important class of large systems arises from the discretization of partial differential equations. In this case, the matrices are sparse (i.e., they contain mostly zeroes) and well-suited to iterative algorithms.
The first edition of this book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics. The second edition includes quite novel approaches.
Описание: Presents the description of the state of the modern iterative techniques together with systematic analysis. This book discusses classical methods, semi-iterative techniques, incomplete decompositions, conjugate gradient methods, multigrid methods and domain decomposition techniques.
Автор: Olshanskii Название: Iterative Methods for Linear Systems ISBN: 1611973457 ISBN-13(EAN): 9781611973457 Издательство: Eurospan Рейтинг: Цена: 10647 р. Наличие на складе: Нет в наличии.
Описание: Systems of linear equations are ubiquitous in numerical analysis and scientific computing. and iterative methods are indispensable for the numerical treatment of such systems. This book offers a rigorous introduction to fundamental iterative methods for systems of linear algebraic equations. The book distinguishes itself from other texts on the topic by providing a straightforward yet comprehensive analysis of the Krylov subspace methods, approaching the development and analysis of algorithms from various perspectives, and going beyond the standard description of iterative methods by connecting them in a natural way to the idea of preconditioning. The book supplements standard texts on numerical mathematics for first-year graduate and advanced undergraduate courses and is suitable for advanced graduate classes covering numerical linear algebra and Krylov subspace and multigrid iterative methods. It will be useful to researchers interested in numerical linear algebra and engineers who use iterative methods for solving large algebraic systems.
Описание: Computational simulation of scientific phenomena and engineering problems often depends on solving linear systems with a large number of unknowns. This book gives insight into the construction of iterative methods for the solution of such systems and helps the reader to select the best solver for a given class of problems. The emphasis is on the main ideas and how they have led to efficient solvers such as CG, GMRES, and BI-CGSTAB. The author also explains the main concepts behind the construction of preconditioners. The reader is encouraged to gain experience by analysing numerous examples that illustrate how best to exploit the methods. The book also hints at many open problems and as such it will appeal to established researchers. There are many exercises that motivate the material and help students to understand the essential steps in the analysis and construction of algorithms.
Описание: Iterative Methods for Queuing and Manufacturing Systems introduces the recent advances and developments in iterative methods for solving Markovian queuing and manufacturing problems.Key highlights include:- an introduction to simulation and simulation software packages;- Markovian models with applications in inventory control and supply chains; future research directions.With numerous exercises and fully-worked examples, this book will be essential reading for anyone interested in the formulation and computation of queuing and manufacturing systems but it will be of particular interest to students, practitioners and researchers in Applied Mathematics, Scientific Computing and Operational Research.
Автор: Ng, Michael K. Название: Iterative Methods for Toeplitz Systems ISBN: 0198504209 ISBN-13(EAN): 9780198504207 Издательство: Oxford Academ Рейтинг: Цена: 14051 р. Наличие на складе: Невозможна поставка.
Описание: Toeplitz and Toeplitz-related systems arise in a variety of applications in mathematics and engineering, especially in signal and image processing. This book deals primarily with iterative methods for solving Toeplitz and Toeplitz-related linear systems, discussing both the algorithms and their convergence theories. A basic knowledge of real analysis, elementary numerical analysis and linear algebra is assumed.
Описание: This book focuses on the approximation of nonlinear equations using iterative methods. Nine contributions are presented on the construction and analysis of these methods, the coverage encompassing convergence, efficiency, robustness, dynamics, and applications. Many problems are stated in the form of nonlinear equations, using mathematical modeling. In particular, a wide range of problems in Applied Mathematics and in Engineering can be solved by finding the solutions to these equations. The book reveals the importance of studying convergence aspects in iterative methods and shows that selection of the most efficient and robust iterative method for a given problem is crucial to guaranteeing a good approximation. A number of sample criteria for selecting the optimal method are presented, including those regarding the order of convergence, the computational cost, and the stability, including the dynamics. This book will appeal to researchers whose field of interest is related to nonlinear problems and equations, and their approximation.
Описание: "This book gives a comprehensive overview of the intersection between ILC and MAS, the range of topics include basic to advanced theories, rigorous mathematics to engineering practice, and linear to nonlinear systems. It addresses the crucial multi-agent coordination and control challenges that can be solved by ILC methods. Through systematic discussion of network theory and intelligent control, the authors explore future research possibilities, develop new tools, and provide numerous applications such as the power grid, communication and sensor networks, intelligent transportation system, and formation control. Readers will gain a roadmap to the latest advances in the fields and use their newfound knowledge to design their own algorithms"--
Автор: Duff I. S Название: Direct Methods for Sparse Matrices ISBN: 0198508387 ISBN-13(EAN): 9780198508380 Издательство: Oxford Academ Рейтинг: Цена: 6349 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The subject of sparse matrices has its root in such diverse fields as management science, power systems analysis, surveying, circuit theory, and structural analysis. Efficient use of sparsity is a key to solving large problems in many fields. This book provides both insight and answers for those attempting to solve these problems.
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