Krylov Methods For Nonsymmetric Linear Systems

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Krylov Methods For Nonsymmetric Linear Systems

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Author : Gérard Meurant
language : en
Publisher: Springer Nature
Release Date : 2020-10-02

Krylov Methods For Nonsymmetric Linear Systems written by Gérard Meurant and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-02 with Mathematics categories.

This book aims to give an encyclopedic overview of the state-of-the-art of Krylov subspace iterative methods for solving nonsymmetric systems of algebraic linear equations and to study their mathematical properties. Solving systems of algebraic linear equations is among the most frequent problems in scientific computing; it is used in many disciplines such as physics, engineering, chemistry, biology, and several others. Krylov methods have progressively emerged as the iterative methods with the highest efficiency while being very robust for solving large linear systems; they may be expected to remain so, independent of progress in modern computer-related fields such as parallel and high performance computing. The mathematical properties of the methods are described and analyzed along with their behavior in finite precision arithmetic. A number of numerical examples demonstrate the properties and the behavior of the described methods. Also considered are the methods’ implementations and coding as Matlab®-like functions. Methods which became popular recently are considered in the general framework of Q-OR (quasi-orthogonal )/Q-MR (quasi-minimum) residual methods. This book can be useful for both practitioners and for readers who are more interested in theory. Together with a review of the state-of-the-art, it presents a number of recent theoretical results of the authors, some of them unpublished, as well as a few original algorithms. Some of the derived formulas might be useful for the design of possible new methods or for future analysis. For the more applied user, the book gives an up-to-date overview of the majority of the available Krylov methods for nonsymmetric linear systems, including well-known convergence properties and, as we said above, template codes that can serve as the base for more individualized and elaborate implementations.

Templates For The Solution Of Linear Systems

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Author : Richard Barrett
language : en
Publisher: SIAM
Release Date : 1994-01-01

Templates For The Solution Of Linear Systems written by Richard Barrett and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-01 with Mathematics categories.

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.

Algorithms For Sparse Linear Systems

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Author : Jennifer Scott
language : en
Publisher: Springer Nature
Release Date : 2023-04-29

Algorithms For Sparse Linear Systems written by Jennifer Scott and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-29 with Mathematics categories.

Large sparse linear systems of equations are ubiquitous in science, engineering and beyond. This open access monograph focuses on factorization algorithms for solving such systems. It presents classical techniques for complete factorizations that are used in sparse direct methods and discusses the computation of approximate direct and inverse factorizations that are key to constructing general-purpose algebraic preconditioners for iterative solvers. A unified framework is used that emphasizes the underlying sparsity structures and highlights the importance of understanding sparse direct methods when developing algebraic preconditioners. Theoretical results are complemented by sparse matrix algorithm outlines. This monograph is aimed at students of applied mathematics and scientific computing, as well as computational scientists and software developers who are interested in understanding the theory and algorithms needed to tackle sparse systems. It is assumed that the reader has completed a basic course in linear algebra and numerical mathematics.

A Journey Through The History Of Numerical Linear Algebra

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Author : Claude Brezinski
language : en
Publisher: SIAM
Release Date : 2022-12-06

A Journey Through The History Of Numerical Linear Algebra written by Claude Brezinski and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-06 with Mathematics categories.

This expansive volume describes the history of numerical methods proposed for solving linear algebra problems, from antiquity to the present day. The authors focus on methods for linear systems of equations and eigenvalue problems and describe the interplay between numerical methods and the computing tools available at the time. The second part of the book consists of 78 biographies of important contributors to the field. A Journey through the History of Numerical Linear Algebra will be of special interest to applied mathematicians, especially researchers in numerical linear algebra, people involved in scientific computing, and historians of mathematics.

High Performance Computing Hipc 2001

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Author : Burkhard Monien
language : en
Publisher: Springer
Release Date : 2001-01-01

High Performance Computing Hipc 2001 written by Burkhard Monien and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Computers categories.

This book constitutes the refereed proceedings of the 8th International Conference on High Performance Computing, HiPC 2001, held in Hyderabad, India, in December 2001.The 29 revised full papers presented together with 5 keynote papers and 3 invited papers were carefully reviewed and selected from 108 submissions. The papers are organized in topical sections on algorithms, applications, architecture, systems software, communications networks, and challenges in networking.

Issues In Algebra Geometry And Topology 2011 Edition

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Author :
language : en
Publisher: ScholarlyEditions
Release Date : 2012-01-09

Issues In Algebra Geometry And Topology 2011 Edition written by and has been published by ScholarlyEditions this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-09 with Mathematics categories.

Issues in Algebra, Geometry, and Topology / 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Algebra, Geometry, and Topology. The editors have built Issues in Algebra, Geometry, and Topology: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Algebra, Geometry, and Topology in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Algebra, Geometry, and Topology: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Numerical Partial Differential Equations

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Author : James H. Adler
language : en
Publisher: SIAM
Release Date : 2025-03-26

Numerical Partial Differential Equations written by James H. Adler and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-26 with Mathematics categories.

This comprehensive textbook focuses on numerical methods for approximating solutions to partial differential equations (PDEs). The authors present a broad survey of these methods, introducing readers to the central concepts of various families of discretizations and solution algorithms and laying the foundation needed to understand more advanced material. The authors include over 100 well-established definitions, theorems, corollaries, and lemmas and summaries of and references to in-depth treatments of more advanced mathematics when needed. Numerical Partial Differential Equations is divided into four parts: Part I covers basic background on PDEs and numerical methods. Part II introduces the three main classes of numerical methods for PDEs that are the book’s focus (finite-difference, finite-element, and finite-volume methods). Part III discusses linear solvers and finite-element and finite-volume methods at a more advanced level. Part IV presents further high-level topics on discretizations and solvers. This book is intended for advanced undergraduate/first-year graduate and advanced graduate students in applied math, as well as students in science and engineering disciplines. The book will also appeal to researchers in the field of scientific computing. Chapters are designed to be stand-alone, allowing distinct paths through the text, making it appropriate for both single-semester and multi-semester courses. It is appropriate for courses covering topics ranging from numerical methods for PDEs to numerical linear algebra.

An Introduction To Domain Decomposition Methods

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Author : Victorita Dolean
language : en
Publisher: SIAM
Release Date : 2015-12-08

An Introduction To Domain Decomposition Methods written by Victorita Dolean and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-08 with Science categories.

The purpose of this book is to offer an overview of the most popular domain decomposition methods for partial differential equations (PDEs). These methods are widely used for numerical simulations in solid mechanics, electromagnetism, flow in porous media, etc., on parallel machines from tens to hundreds of thousands of cores. The appealing feature of domain decomposition methods is that, contrary to direct methods, they are naturally parallel. The authors focus on parallel linear solvers. The authors present all popular algorithms, both at the PDE level and at the discrete level in terms of matrices, along with systematic scripts for sequential implementation in a free open-source finite element package as well as some parallel scripts. Also included is a new coarse space construction (two-level method) that adapts to highly heterogeneous problems.?

Krylov Methods For The Numerical Solution Of Initial Value Problems In Differential Algebraic Equations

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Author : Steven Lewis Lee
language : en
Publisher:
Release Date : 1993

Krylov Methods For The Numerical Solution Of Initial Value Problems In Differential Algebraic Equations written by Steven Lewis Lee and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.

Computational Science Iccs 2007

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Author : Yong Shi
language : en
Publisher: Springer
Release Date : 2007-07-14

Computational Science Iccs 2007 written by Yong Shi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-14 with Computers categories.

Part of a four-volume set, this book constitutes the refereed proceedings of the 7th International Conference on Computational Science, ICCS 2007, held in Beijing, China in May 2007. The papers cover a large volume of topics in computational science and related areas, from multiscale physics to wireless networks, and from graph theory to tools for program development.