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Author : Louis A. Hageman
Publisher : Elsevier
Page : 409 pages
File Size : 51,7 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9781483294377
Applied Iterative Methods
Author : CHARLES L. BYRNE
Publisher : A K PETERS
Page : 400 pages
File Size : 48,5 Mb
Release : 2021-09-30
Category : Electronic
ISBN : 0367446162
This book is a collection of essays on iterative algorithms and their uses. It focuses on the mathematics of medical image reconstruction, with emphasis on Fourier inversion. The book discusses the problems and algorithms in the context of operators on finite-dimensional Euclidean space.
Author : Yousef Saad
Publisher : SIAM
Page : 537 pages
File Size : 49,7 Mb
Release : 2003-04-01
Category : Mathematics
ISBN : 9780898715347
Mathematics of Computing -- General.
Author : C. T. Kelley
Publisher : SIAM
Page : 179 pages
File Size : 53,5 Mb
Release : 1995-01-01
Category : Mathematics
ISBN : 1611970946
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. Examples, methods, and algorithmic choices are based on applications to infinite dimensional problems such as partial differential equations and integral equations. The analysis and proof techniques are constructed with the infinite dimensional setting in mind and the computational examples and exercises are based on the MATLAB environment.
Author : Anne Greenbaum
Publisher : SIAM
Page : 225 pages
File Size : 54,7 Mb
Release : 1997-01-01
Category : Mathematics
ISBN : 9780898713961
Mathematics of Computing -- Numerical Analysis.
Author : C. T. Kelley
Publisher : SIAM
Page : 195 pages
File Size : 40,8 Mb
Release : 1999-01-01
Category : Mathematics
ISBN : 161197092X
This book presents a carefully selected group of methods for unconstrained and bound constrained optimization problems and analyzes them in depth both theoretically and algorithmically. It focuses on clarity in algorithmic description and analysis rather than generality, and while it provides pointers to the literature for the most general theoretical results and robust software, the author thinks it is more important that readers have a complete understanding of special cases that convey essential ideas. A companion to Kelley's book, Iterative Methods for Linear and Nonlinear Equations (SIAM, 1995), this book contains many exercises and examples and can be used as a text, a tutorial for self-study, or a reference. Iterative Methods for Optimization does more than cover traditional gradient-based optimization: it is the first book to treat sampling methods, including the Hooke-Jeeves, implicit filtering, MDS, and Nelder-Mead schemes in a unified way, and also the first book to make connections between sampling methods and the traditional gradient-methods. Each of the main algorithms in the text is described in pseudocode, and a collection of MATLAB codes is available. Thus, readers can experiment with the algorithms in an easy way as well as implement them in other languages.
Author : Richard Barrett,Michael W. Berry,Tony F. Chan,James Demmel,June Donato,Jack Dongarra,Victor Eijkhout,Roldan Pozo,Charles Romine,Henk van der Vorst
Publisher : SIAM
Page : 141 pages
File Size : 50,8 Mb
Release : 1994-01-01
Category : Mathematics
ISBN : 1611971535
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 : Maxim A. Olshanskii,Eugene E. Tyrtyshnikov
Publisher : SIAM
Page : 257 pages
File Size : 48,5 Mb
Release : 2014-07-21
Category : Mathematics
ISBN : 9781611973464
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 : H. A. van der Vorst
Publisher : Cambridge University Press
Page : 242 pages
File Size : 47,9 Mb
Release : 2003-04-17
Category : Mathematics
ISBN : 0521818281
Table of contents
Author : Gabriele Ciaramella,Martin J. Gander
Publisher : SIAM
Page : 285 pages
File Size : 49,5 Mb
Release : 2022-02-08
Category : Mathematics
ISBN : 9781611976908
Iterative methods use successive approximations to obtain more accurate solutions. This book gives an introduction to iterative methods and preconditioning for solving discretized elliptic partial differential equations and optimal control problems governed by the Laplace equation, for which the use of matrix-free procedures is crucial. All methods are explained and analyzed starting from the historical ideas of the inventors, which are often quoted from their seminal works. Iterative Methods and Preconditioners for Systems of Linear Equations grew out of a set of lecture notes that were improved and enriched over time, resulting in a clear focus for the teaching methodology, which derives complete convergence estimates for all methods, illustrates and provides MATLAB codes for all methods, and studies and tests all preconditioners first as stationary iterative solvers. This textbook is appropriate for undergraduate and graduate students who want an overview or deeper understanding of iterative methods. Its focus on both analysis and numerical experiments allows the material to be taught with very little preparation, since all the arguments are self-contained, and makes it appropriate for self-study as well. It can be used in courses on iterative methods, Krylov methods and preconditioners, and numerical optimal control. Scientists and engineers interested in new topics and applications will also find the text useful.
Author : James W. Demmel
Publisher : SIAM
Page : 426 pages
File Size : 42,8 Mb
Release : 1997-08-01
Category : Mathematics
ISBN : 9780898713893
This comprehensive textbook is designed for first-year graduate students from a variety of engineering and scientific disciplines.
Author : Louis A. Hageman
Publisher : Unknown
Page : 128 pages
File Size : 44,7 Mb
Release : 2004
Category : Electronic
ISBN : OCLC:985928740
Author : Daniele Bertaccini,Fabio Durastante
Publisher : CRC Press
Page : 366 pages
File Size : 45,6 Mb
Release : 2018-02-19
Category : Mathematics
ISBN : 9781351649612
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 : Lap Chi Lau,R. Ravi,Mohit Singh
Publisher : Cambridge University Press
Page : 255 pages
File Size : 55,5 Mb
Release : 2011-04-18
Category : Computers
ISBN : 9781139499392
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.
Author : Are Magnus Bruaset
Publisher : Routledge
Page : 140 pages
File Size : 55,5 Mb
Release : 2018-12-13
Category : Mathematics
ISBN : 9781351469364
The problem of solving large, sparse, linear systems of algebraic equations is vital in scientific computing, even for applications originating from quite different fields. A Survey of Preconditioned Iterative Methods presents an up to date overview of iterative methods for numerical solution of such systems. Typically, the methods considered are w
