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| Author | : Yousef Saad |
| Publisher | : SIAM |
| Total Pages | : 537 |
| Release | : 2003-04-01 |
| Genre | : Mathematics |
| ISBN | : 0898715342 |
Mathematics of Computing -- General.
| Author | : H. A. van der Vorst |
| Publisher | : Cambridge University Press |
| Total Pages | : 242 |
| Release | : 2003-04-17 |
| Genre | : Mathematics |
| ISBN | : 9780521818285 |
Table of contents
| Author | : David M. Young |
| Publisher | : Elsevier |
| Total Pages | : 599 |
| Release | : 2014-05-10 |
| Genre | : Mathematics |
| ISBN | : 1483274136 |
Iterative Solution of Large Linear Systems describes the systematic development of a substantial portion of the theory of iterative methods for solving large linear systems, with emphasis on practical techniques. The focal point of the book is an analysis of the convergence properties of the successive overrelaxation (SOR) method as applied to a linear system where the matrix is "consistently ordered". Comprised of 18 chapters, this volume begins by showing how the solution of a certain partial differential equation by finite difference methods leads to a large linear system with a sparse matrix. The next chapter reviews matrix theory and the properties of matrices, as well as several theorems of matrix theory without proof. A number of iterative methods, including the SOR method, are then considered. Convergence theorems are also given for various iterative methods under certain assumptions on the matrix A of the system. Subsequent chapters deal with the eigenvalues of the SOR method for consistently ordered matrices; the optimum relaxation factor; nonstationary linear iterative methods; and semi-iterative methods. This book will be of interest to students and practitioners in the fields of computer science and applied mathematics.
| Author | : Maxim A. Olshanskii |
| Publisher | : SIAM |
| Total Pages | : 257 |
| Release | : 2014-07-21 |
| Genre | : Mathematics |
| ISBN | : 1611973465 |
Iterative Methods for Linear Systems?offers a mathematically 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 algorithmic and mathematical perspectives, and going beyond the standard description of iterative methods by connecting them in a natural way to the idea of preconditioning.??
| Author | : Anne Greenbaum |
| Publisher | : SIAM |
| Total Pages | : 225 |
| Release | : 1997-01-01 |
| Genre | : Mathematics |
| ISBN | : 089871396X |
Mathematics of Computing -- Numerical Analysis.
| Author | : Richard Barrett |
| Publisher | : SIAM |
| Total Pages | : 141 |
| Release | : 1994-01-01 |
| Genre | : Mathematics |
| ISBN | : 9781611971538 |
In this book, which focuses on the use of iterative methods for solving large sparse systems of linear equations, templates are introduced to meet the needs of both the traditional user and the high-performance specialist. Templates, a description of a general algorithm rather than the executable object or source code more commonly found in a conventional software library, offer whatever degree of customization the user may desire. Templates offer three distinct advantages: they are general and reusable; they are not language specific; and they exploit the expertise of both the numerical analyst, who creates a template reflecting in-depth knowledge of a specific numerical technique, and the computational scientist, who then provides "value-added" capability to the general template description, customizing it for specific needs. For each template that is presented, the authors provide: a mathematical description of the flow of algorithm; discussion of convergence and stopping criteria to use in the iteration; suggestions for applying a method to special matrix types; advice for tuning the template; tips on parallel implementations; and hints as to when and why a method is useful.
| Author | : Daniele Bertaccini |
| Publisher | : CRC Press |
| Total Pages | : 321 |
| Release | : 2018-02-19 |
| Genre | : Mathematics |
| ISBN | : 1351649612 |
This book describes, in a basic way, the most useful and effective iterative solvers and appropriate preconditioning techniques for some of the most important classes of large and sparse linear systems. The solution of large and sparse linear systems is the most time-consuming part for most of the scientific computing simulations. Indeed, mathematical models become more and more accurate by including a greater volume of data, but this requires the solution of larger and harder algebraic systems. In recent years, research has focused on the efficient solution of large sparse and/or structured systems generated by the discretization of numerical models by using iterative solvers.
| Author | : David Ronald Kincaid |
| Publisher | : |
| Total Pages | : 360 |
| Release | : 1990 |
| Genre | : Mathematics |
| ISBN | : |
Very Good,No Highlights or Markup,all pages are intact.
| Author | : Louis A. Hageman |
| Publisher | : Elsevier |
| Total Pages | : 409 |
| Release | : 2014-06-28 |
| Genre | : Mathematics |
| ISBN | : 1483294374 |
Applied Iterative Methods
| Author | : David R. Kincaid |
| Publisher | : Academic Press |
| Total Pages | : 350 |
| Release | : 2014-05-10 |
| Genre | : Mathematics |
| ISBN | : 1483260208 |
Iterative Methods for Large Linear Systems contains a wide spectrum of research topics related to iterative methods, such as searching for optimum parameters, using hierarchical basis preconditioners, utilizing software as a research tool, and developing algorithms for vector and parallel computers. This book provides an overview of the use of iterative methods for solving sparse linear systems, identifying future research directions in the mainstream of modern scientific computing with an eye to contributions of the past, present, and future. Different iterative algorithms that include the successive overrelaxation (SOR) method, symmetric and unsymmetric SOR methods, local (ad-hoc) SOR scheme, and alternating direction implicit (ADI) method are also discussed. This text likewise covers the block iterative methods, asynchronous iterative procedures, multilevel methods, adaptive algorithms, and domain decomposition algorithms. This publication is a good source for mathematicians and computer scientists interested in iterative methods for large linear systems.
