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: 11900 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 scientists often encounter problems requiring the solution of sparse systems of linear equations. Attacking these problems efficiently requires an in-depth knowledge of the underlying theory, algorithms, and data structures found in sparse matrix software libraries. Here, Davis presents the fundamentals of sparse matrix algorithms to provide the requisite background. The book includes CSparse, a concise downloadable sparse matrix package that illustrates the algorithms and theorems presented in the book and equips readers with the tools necessary to understand larger and more complex software packages. With a strong emphasis on MATLAB?® and the C programming language, Direct Methods for Sparse Linear Systems equips readers with the working knowledge required to use sparse solver packages and write code to interface applications to those packages. The book also explains how MATLAB performs its sparse matrix computations.
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.
Описание: Linear and nonlinear systems of equations are the basis for many, if not most, of the models of phenomena in science and engineering, and their efficient numerical solution is critical to progress in these areas. This is the first book to be published on nonlinear equations since the mid-1980s. Although it stresses recent developments in this area, such as Newton-Krylov methods, considerable material on linear equations has been incorporated. This book focuses on a small number of methods and treats them in depth. The author provides a complete analysis of the conjugate gradient and generalized minimum residual iterations as well as recent advances including Newton-Krylov methods, incorporation of inexactness and noise into the analysis, new proofs and implementations of Broyden's method, and globalization of inexact Newton methods.
Описание: This textbook should be useful for graduate students, practicing engineers, and researchers who wish to thoroughly understand the detailed step-by-step algorithms, used during the finite element (truly sparse) assembly, the "direct" and "iterative" sparse equation * eigen-solvers and incorporating the DD formulation for efficient parallel computation.
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.
Автор: Ng, Michael K. Название: Iterative Methods for Toeplitz Systems ISBN: 0198504209 ISBN-13(EAN): 9780198504207 Издательство: Oxford Academ Рейтинг: Цена: 15530 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: 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.