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Author: Ke Chen
Publisher: Cambridge University Press
ISBN: 9780521838283
Category : Mathematics
Languages : en
Pages : 616
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Book Description
A comprehensive introduction to preconditioning techniques, now an essential part of successful and efficient iterative solutions of matrices.
Author: Ke Chen
Publisher: Cambridge University Press
ISBN: 9780521838283
Category : Mathematics
Languages : en
Pages : 616
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Book Description
A comprehensive introduction to preconditioning techniques, now an essential part of successful and efficient iterative solutions of matrices.
Author: Daniele Bertaccini
Publisher: CRC Press
ISBN: 1351649612
Category : Mathematics
Languages : en
Pages : 321
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Book Description
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: Yousef Saad
Publisher: SIAM
ISBN: 0898715342
Category : Mathematics
Languages : en
Pages : 537
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Book Description
Mathematics of Computing -- General.
Author: Josef Malek
Publisher: SIAM
ISBN: 161197383X
Category : Mathematics
Languages : en
Pages : 106
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Book Description
Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs?is about the interplay between modeling, analysis, discretization, matrix computation, and model reduction. The authors link PDE analysis, functional analysis, and calculus of variations with matrix iterative computation using Krylov subspace methods and address the challenges that arise during formulation of the mathematical model through to efficient numerical solution of the algebraic problem. The book?s central concept, preconditioning of the conjugate gradient method, is traditionally developed algebraically using the preconditioned finite-dimensional algebraic system. In this text, however, preconditioning is connected to the PDE analysis, and the infinite-dimensional formulation of the conjugate gradient method and its discretization and preconditioning are linked together. This text challenges commonly held views, addresses widespread misunderstandings, and formulates thought-provoking open questions for further research.?
Author: Vadim Olshevsky
Publisher: World Scientific
ISBN: 9814469556
Category : Mathematics
Languages : en
Pages : 604
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Book Description
Compared to other books devoted to matrices, this volume is unique in covering the whole of a triptych consisting of algebraic theory, algorithmic problems and numerical applications, all united by the essential use and urge for development of matrix methods. This was the spirit of the 2nd International Conference on Matrix Methods and Operator Equations from 23-27 July 2007 in Moscow that was organized by Dario Bini, Gene Golub, Alexander Guterman, Vadim Olshevsky, Stefano Serra-Capizzano, Gilbert Strang and Eugene Tyrtyshnikov.Matrix methods provide the key to many problems in pure and applied mathematics. However, linear algebra theory, numerical algorithms and matrices in FEM/BEM applications usually live as if in three separate worlds. In this volume, maybe for the first time ever, they are compiled together as one entity as it was at the Moscow meeting, where the algebraic part was impersonated by Hans Schneider, algorithms by Gene Golub, and applications by Guri Marchuk. All topics intervened in plenary sessions are specially categorized into three sections of this volume.The soul of the meeting was Gene Golub, who rendered a charming “Golub's dimension” to the three main axes of the conference topics. This volume is dedicated in gratitude to his memory.
Author: Wilhelmus H. Schilders
Publisher: Springer Science & Business Media
ISBN: 3540788417
Category : Mathematics
Languages : en
Pages : 471
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Book Description
The idea for this book originated during the workshop “Model order reduction, coupled problems and optimization” held at the Lorentz Center in Leiden from S- tember 19–23, 2005. During one of the discussion sessions, it became clear that a book describing the state of the art in model order reduction, starting from the very basics and containing an overview of all relevant techniques, would be of great use for students, young researchers starting in the ?eld, and experienced researchers. The observation that most of the theory on model order reduction is scattered over many good papers, making it dif?cult to ?nd a good starting point, was supported by most of the participants. Moreover, most of the speakers at the workshop were willing to contribute to the book that is now in front of you. The goal of this book, as de?ned during the discussion sessions at the workshop, is three-fold: ?rst, it should describe the basics of model order reduction. Second, both general and more specialized model order reduction techniques for linear and nonlinear systems should be covered, including the use of several related numerical techniques. Third, the use of model order reduction techniques in practical appli- tions and current research aspects should be discussed. We have organized the book according to these goals. In Part I, the rationale behind model order reduction is explained, and an overview of the most common methods is described.
Author: Maxim A. Olshanskii
Publisher: SIAM
ISBN: 1611973465
Category : Mathematics
Languages : en
Pages : 257
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Book Description
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: Ke Chen
Publisher:
ISBN: 9781139444101
Category : Differential equations
Languages : en
Pages :
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Book Description
Author: H. A. van der Vorst
Publisher: Cambridge University Press
ISBN: 9780521818285
Category : Mathematics
Languages : en
Pages : 242
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Book Description
Table of contents
Author: Jochen Pfalzgraf
Publisher: Springer Science & Business Media
ISBN: 3709166047
Category : Computers
Languages : en
Pages : 233
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Book Description
This book is a collection of selected papers written by researchers qf our "RISC" institute (Research Institute for Symbolic Computation) along with the ESPRIT MEDLAR Project (Mechanizing Deduction in the Logics of Practical Reason ing). Naturally, the MEDLAR Project was and is the focal point for our institute whose main objective is the combination of foundational research in the area of symbolic computation and possible applications thereof for high-tech industrial projects. I am grateful to the director of the MEDLAR project, Jim Cunningham, for his enthusiasm, profound expertise, and continuous effort to manage a fruitful cooperation between various European working groups in the area of the project and for giving us the opportunity to be part of this challenging endeavor. I also acknowledge and feel indebted to Jochen Pfalzgraf for managing the RISC part of the MEDLAR project and to both him and Dongming Wang for editing this volume and organizing the refereeing process.
