Templates For The Solution Of Linear Systems

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Templates for the Solution of Linear Systems

Richard Barrett,Michael W. Berry,Tony F. Chan,James Demmel,June Donato,Jack Dongarra,Victor Eijkhout,Roldan Pozo,Charles Romine,Henk van der Vorst
Templates for the Solution of Linear Systems Book PDF

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 : 46,6 Mb
Release : 1994-01-01
Category : Mathematics
ISBN : 1611971535

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Templates for the Solution of Linear Systems by Richard Barrett,Michael W. Berry,Tony F. Chan,James Demmel,June Donato,Jack Dongarra,Victor Eijkhout,Roldan Pozo,Charles Romine,Henk van der Vorst Pdf

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.

Templates for the Solution of Algebraic Eigenvalue Problems

Zhaojun Bai,James Demmel,Jack Dongarra,Axel Ruhe,Henk van der Vorst
Templates for the Solution of Algebraic Eigenvalue Problems Book PDF

Author : Zhaojun Bai,James Demmel,Jack Dongarra,Axel Ruhe,Henk van der Vorst
Publisher : SIAM
Page : 430 pages
File Size : 51,8 Mb
Release : 2000-01-01
Category : Computers
ISBN : 9780898714715

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Templates for the Solution of Algebraic Eigenvalue Problems by Zhaojun Bai,James Demmel,Jack Dongarra,Axel Ruhe,Henk van der Vorst Pdf

Mathematics of Computing -- Numerical Analysis.

Iterative Krylov Methods for Large Linear Systems

H. A. van der Vorst
Iterative Krylov Methods for Large Linear Systems Book PDF

Author : H. A. van der Vorst
Publisher : Cambridge University Press
Page : 242 pages
File Size : 48,7 Mb
Release : 2003-04-17
Category : Mathematics
ISBN : 0521818281

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Iterative Krylov Methods for Large Linear Systems by H. A. van der Vorst Pdf

Table of contents

Matrix Iterative Analysis

Richard S Varga
Matrix Iterative Analysis Book PDF

Author : Richard S Varga
Publisher : Springer Science & Business Media
Page : 363 pages
File Size : 42,9 Mb
Release : 2009-12-05
Category : Mathematics
ISBN : 9783642051562

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Matrix Iterative Analysis by Richard S Varga Pdf

This book is a revised version of the first edition, regarded as a classic in its field. In some places, newer research results have been incorporated in the revision, and in other places, new material has been added to the chapters in the form of additional up-to-date references and some recent theorems to give readers some new directions to pursue.

Applied Numerical Linear Algebra

James W. Demmel
Applied Numerical Linear Algebra Book PDF

Author : James W. Demmel
Publisher : SIAM
Page : 426 pages
File Size : 46,6 Mb
Release : 1997-08-01
Category : Mathematics
ISBN : 9780898713893

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Applied Numerical Linear Algebra by James W. Demmel Pdf

This comprehensive textbook is designed for first-year graduate students from a variety of engineering and scientific disciplines.

Parallel Numerical Algorithms

David E. Keyes,Ahmed Sameh,V. Venkatakrishnan
Parallel Numerical Algorithms Book PDF

Author : David E. Keyes,Ahmed Sameh,V. Venkatakrishnan
Publisher : Springer Science & Business Media
Page : 403 pages
File Size : 51,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401154123

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Parallel Numerical Algorithms by David E. Keyes,Ahmed Sameh,V. Venkatakrishnan Pdf

In this volume, designed for computational scientists and engineers working on applications requiring the memories and processing rates of large-scale parallelism, leading algorithmicists survey their own field-defining contributions, together with enough historical and bibliographical perspective to permit working one's way to the frontiers. This book is distinguished from earlier surveys in parallel numerical algorithms by its extension of coverage beyond core linear algebraic methods into tools more directly associated with partial differential and integral equations - though still with an appealing generality - and by its focus on practical medium-granularity parallelism, approachable through traditional programming languages. Several of the authors used their invitation to participate as a chance to stand back and create a unified overview, which nonspecialists will appreciate.

The Symmetric Eigenvalue Problem

Beresford N. Parlett
The Symmetric Eigenvalue Problem Book PDF

Author : Beresford N. Parlett
Publisher : SIAM
Page : 422 pages
File Size : 55,7 Mb
Release : 1998-01-01
Category : Mathematics
ISBN : 1611971160

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The Symmetric Eigenvalue Problem by Beresford N. Parlett Pdf

According to Parlett, "Vibrations are everywhere, and so too are the eigenvalues associated with them. As mathematical models invade more and more disciplines, we can anticipate a demand for eigenvalue calculations in an ever richer variety of contexts." Anyone who performs these calculations will welcome the reprinting of Parlett's book (originally published in 1980). In this unabridged, amended version, Parlett covers aspects of the problem that are not easily found elsewhere. The chapter titles convey the scope of the material succinctly. The aim of the book is to present mathematical knowledge that is needed in order to understand the art of computing eigenvalues of real symmetric matrices, either all of them or only a few. The author explains why the selected information really matters and he is not shy about making judgments. The commentary is lively but the proofs are terse. The first nine chapters are based on a matrix on which it is possible to make similarity transformations explicitly. The only source of error is inexact arithmetic. The last five chapters turn to large sparse matrices and the task of making approximations and judging them.

Applied Parallel Computing

Bo Kagström,Erik Elmroth,Jack Dongarra,Jerzy Wasniewski
Applied Parallel Computing Book PDF

Author : Bo Kagström,Erik Elmroth,Jack Dongarra,Jerzy Wasniewski
Publisher : Springer
Page : 1192 pages
File Size : 46,6 Mb
Release : 2007-09-22
Category : Computers
ISBN : 9783540757559

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Applied Parallel Computing by Bo Kagström,Erik Elmroth,Jack Dongarra,Jerzy Wasniewski Pdf

This book constitutes the thoroughly refereed post-proceedings of the 8th International Workshop on Applied Parallel Computing, PARA 2006. It covers partial differential equations, parallel scientific computing algorithms, linear algebra, simulation environments, algorithms and applications for blue gene/L, scientific computing tools and applications, parallel search algorithms, peer-to-peer computing, mobility and security, algorithms for single-chip multiprocessors.

Introduction to Applied Linear Algebra

Stephen Boyd,Lieven Vandenberghe
Introduction to Applied Linear Algebra Book PDF

Author : Stephen Boyd,Lieven Vandenberghe
Publisher : Cambridge University Press
Page : 477 pages
File Size : 55,6 Mb
Release : 2018-06-07
Category : Business & Economics
ISBN : 9781316518960

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Introduction to Applied Linear Algebra by Stephen Boyd,Lieven Vandenberghe Pdf

A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

High Performance Computing for Computational Science -- VECPAR 2010

José M. Laginha M. Palma,Michel Daydé,Osni Marques,Joao Correia Lopes
High Performance Computing for Computational Science VECPAR 2010 Book PDF

Author : José M. Laginha M. Palma,Michel Daydé,Osni Marques,Joao Correia Lopes
Publisher : Springer Science & Business Media
Page : 483 pages
File Size : 55,9 Mb
Release : 2011-02-23
Category : Computers
ISBN : 9783642193279

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High Performance Computing for Computational Science -- VECPAR 2010 by José M. Laginha M. Palma,Michel Daydé,Osni Marques,Joao Correia Lopes Pdf

This book constitutes the thoroughly refereed post-conference proceedings of the 9th International Conference on High Performance Computing for Computational Science, VECPAR 2010, held in Berkeley, CA, USA, in June 2010. The 34 revised full papers presented together with five invited contributions were carefully selected during two rounds of reviewing and revision. The papers are organized in topical sections on linear algebra and solvers on emerging architectures, large-scale simulations, parallel and distributed computing, numerical algorithms.

Ordinary Differential Equations: Basics and Beyond

David G. Schaeffer,John W. Cain
Ordinary Differential Equations Basics and Beyond Book PDF

Author : David G. Schaeffer,John W. Cain
Publisher : Springer
Page : 542 pages
File Size : 50,9 Mb
Release : 2016-11-10
Category : Mathematics
ISBN : 9781493963898

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Ordinary Differential Equations: Basics and Beyond by David G. Schaeffer,John W. Cain Pdf

This book develops the theory of ordinary differential equations (ODEs), starting from an introductory level (with no prior experience in ODEs assumed) through to a graduate-level treatment of the qualitative theory, including bifurcation theory (but not chaos). While proofs are rigorous, the exposition is reader-friendly, aiming for the informality of face-to-face interactions. A unique feature of this book is the integration of rigorous theory with numerous applications of scientific interest. Besides providing motivation, this synthesis clarifies the theory and enhances scientific literacy. Other features include: (i) a wealth of exercises at various levels, along with commentary that explains why they matter; (ii) figures with consistent color conventions to identify nullclines, periodic orbits, stable and unstable manifolds; and (iii) a dedicated website with software templates, problem solutions, and other resources supporting the text (www.math.duke.edu/ode-book). Given its many applications, the book may be used comfortably in science and engineering courses as well as in mathematics courses. Its level is accessible to upper-level undergraduates but still appropriate for graduate students. The thoughtful presentation, which anticipates many confusions of beginning students, makes the book suitable for a teaching environment that emphasizes self-directed, active learning (including the so-called inverted classroom).

The Lanczos Method

Louis Komzsik
The Lanczos Method Book PDF

Author : Louis Komzsik
Publisher : SIAM
Page : 99 pages
File Size : 41,5 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 089871818X

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The Lanczos Method by Louis Komzsik Pdf

The Lanczos Method: Evolution and Application is divided into two distinct parts. The first part reviews the evolution of one of the most widely used numerical techniques in the industry. The development of the method, as it became more robust, is demonstrated through easy-to-understand algorithms. The second part contains industrial applications drawn from the author's experience. These chapters provide a unique interaction between the numerical algorithms and their engineering applications.

Automated Solution of Differential Equations by the Finite Element Method

Anders Logg,Kent-Andre Mardal,Garth Wells
Automated Solution of Differential Equations by the Finite Element Method Book PDF

Author : Anders Logg,Kent-Andre Mardal,Garth Wells
Publisher : Springer Science & Business Media
Page : 723 pages
File Size : 52,5 Mb
Release : 2012-02-24
Category : Computers
ISBN : 9783642230998

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Automated Solution of Differential Equations by the Finite Element Method by Anders Logg,Kent-Andre Mardal,Garth Wells Pdf

This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.

Solving ODEs with MATLAB

Lawrence F. Shampine,I. Gladwell,S. Thompson
Solving ODEs with MATLAB Book PDF

Author : Lawrence F. Shampine,I. Gladwell,S. Thompson
Publisher : Cambridge University Press
Page : 276 pages
File Size : 40,5 Mb
Release : 2003-04-28
Category : Computers
ISBN : 0521530946

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Solving ODEs with MATLAB by Lawrence F. Shampine,I. Gladwell,S. Thompson Pdf

This concise text, first published in 2003, is for a one-semester course for upper-level undergraduates and beginning graduate students in engineering, science, and mathematics, and can also serve as a quick reference for professionals. The major topics in ordinary differential equations, initial value problems, boundary value problems, and delay differential equations, are usually taught in three separate semester-long courses. This single book provides a sound treatment of all three in fewer than 300 pages. Each chapter begins with a discussion of the 'facts of life' for the problem, mainly by means of examples. Numerical methods for the problem are then developed, but only those methods most widely used. The treatment of each method is brief and technical issues are minimized, but all the issues important in practice and for understanding the codes are discussed. The last part of each chapter is a tutorial that shows how to solve problems by means of small, but realistic, examples.

Templates for the Solution of Algebraic Eigenvalue Problems

Zhaojun Bai,James Demmel,Jack Dongarra,Axel Ruhe,Henk van der Vorst
Templates for the Solution of Algebraic Eigenvalue Problems Book PDF

Author : Zhaojun Bai,James Demmel,Jack Dongarra,Axel Ruhe,Henk van der Vorst
Publisher : SIAM
Page : 439 pages
File Size : 47,6 Mb
Release : 2000-01-01
Category : Computers
ISBN : 0898719585

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Templates for the Solution of Algebraic Eigenvalue Problems by Zhaojun Bai,James Demmel,Jack Dongarra,Axel Ruhe,Henk van der Vorst Pdf

Large-scale problems of engineering and scientific computing often require solutions of eigenvalue and related problems. This book gives a unified overview of theory, algorithms, and practical software for eigenvalue problems. It organizes this large body of material to make it accessible for the first time to the many nonexpert users who need to choose the best state-of-the-art algorithms and software for their problems. Using an informal decision tree, just enough theory is introduced to identify the relevant mathematical structure that determines the best algorithm for each problem.