Introduction to Parallel and Vector Solution of Linear Systems

Introduction to Parallel and Vector Solution of Linear Systems

Author: James M. Ortega

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 309

ISBN-13: 1489921125

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Although the origins of parallel computing go back to the last century, it was only in the 1970s that parallel and vector computers became available to the scientific community. The first of these machines-the 64 processor llliac IV and the vector computers built by Texas Instruments, Control Data Corporation, and then CRA Y Research Corporation-had a somewhat limited impact. They were few in number and available mostly to workers in a few government laboratories. By now, however, the trickle has become a flood. There are over 200 large-scale vector computers now installed, not only in government laboratories but also in universities and in an increasing diversity of industries. Moreover, the National Science Foundation's Super computing Centers have made large vector computers widely available to the academic community. In addition, smaller, very cost-effective vector computers are being manufactured by a number of companies. Parallelism in computers has also progressed rapidly. The largest super computers now consist of several vector processors working in parallel. Although the number of processors in such machines is still relatively small (up to 8), it is expected that an increasing number of processors will be added in the near future (to a total of 16 or 32). Moreover, there are a myriad of research projects to build machines with hundreds, thousands, or even more processors. Indeed, several companies are now selling parallel machines, some with as many as hundreds, or even tens of thousands, of processors.


Book Synopsis Introduction to Parallel and Vector Solution of Linear Systems by : James M. Ortega

Download or read book Introduction to Parallel and Vector Solution of Linear Systems written by James M. Ortega and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the origins of parallel computing go back to the last century, it was only in the 1970s that parallel and vector computers became available to the scientific community. The first of these machines-the 64 processor llliac IV and the vector computers built by Texas Instruments, Control Data Corporation, and then CRA Y Research Corporation-had a somewhat limited impact. They were few in number and available mostly to workers in a few government laboratories. By now, however, the trickle has become a flood. There are over 200 large-scale vector computers now installed, not only in government laboratories but also in universities and in an increasing diversity of industries. Moreover, the National Science Foundation's Super computing Centers have made large vector computers widely available to the academic community. In addition, smaller, very cost-effective vector computers are being manufactured by a number of companies. Parallelism in computers has also progressed rapidly. The largest super computers now consist of several vector processors working in parallel. Although the number of processors in such machines is still relatively small (up to 8), it is expected that an increasing number of processors will be added in the near future (to a total of 16 or 32). Moreover, there are a myriad of research projects to build machines with hundreds, thousands, or even more processors. Indeed, several companies are now selling parallel machines, some with as many as hundreds, or even tens of thousands, of processors.


Scientific Computing

Scientific Computing

Author: Gene H. Golub

Publisher: Elsevier

Published: 2014-06-28

Total Pages: 442

ISBN-13: 1483296040

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This book introduces the basic concepts of parallel and vector computing in the context of an introduction to numerical methods. It contains chapters on parallel and vector matrix multiplication and solution of linear systems by direct and iterative methods. It is suitable for advanced undergraduate and beginning graduate courses in computer science, applied mathematics, and engineering. Ideally, students will have access to a parallel or Vector computer, but the material can be studied profitably in any case. Gives a modern overview of scientific computing including parallel an vector computation Introduces numerical methods for both ordinary and partial differential equations Has considerable discussion of both direct and iterative methods for linear systems of equations, including parallel and vector algorithms Covers most of the main topics for a first course in numerical methods and can serve as a text for this course


Book Synopsis Scientific Computing by : Gene H. Golub

Download or read book Scientific Computing written by Gene H. Golub and published by Elsevier. This book was released on 2014-06-28 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the basic concepts of parallel and vector computing in the context of an introduction to numerical methods. It contains chapters on parallel and vector matrix multiplication and solution of linear systems by direct and iterative methods. It is suitable for advanced undergraduate and beginning graduate courses in computer science, applied mathematics, and engineering. Ideally, students will have access to a parallel or Vector computer, but the material can be studied profitably in any case. Gives a modern overview of scientific computing including parallel an vector computation Introduces numerical methods for both ordinary and partial differential equations Has considerable discussion of both direct and iterative methods for linear systems of equations, including parallel and vector algorithms Covers most of the main topics for a first course in numerical methods and can serve as a text for this course


Solution of Partial Differential Equations on Vector and Parallel Computers

Solution of Partial Differential Equations on Vector and Parallel Computers

Author: James M. Ortega

Publisher: SIAM

Published: 1985-09-01

Total Pages: 99

ISBN-13: 0898710553

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Mathematics of Computing -- Parallelism.


Book Synopsis Solution of Partial Differential Equations on Vector and Parallel Computers by : James M. Ortega

Download or read book Solution of Partial Differential Equations on Vector and Parallel Computers written by James M. Ortega and published by SIAM. This book was released on 1985-09-01 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Parallelism.


Iterative Krylov Methods for Large Linear Systems

Iterative Krylov Methods for Large Linear Systems

Author: H. A. van der Vorst

Publisher: Cambridge University Press

Published: 2003-04-17

Total Pages: 242

ISBN-13: 9780521818285

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Table of contents


Book Synopsis Iterative Krylov Methods for Large Linear Systems by : H. A. van der Vorst

Download or read book Iterative Krylov Methods for Large Linear Systems written by H. A. van der Vorst and published by Cambridge University Press. This book was released on 2003-04-17 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of contents


Matrix Computations

Matrix Computations

Author: Gene H. Golub

Publisher: JHU Press

Published: 1996-10-15

Total Pages: 734

ISBN-13: 9780801854149

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Revised and updated, the third edition of Golub and Van Loan's classic text in computer science provides essential information about the mathematical background and algorithmic skills required for the production of numerical software. This new edition includes thoroughly revised chapters on matrix multiplication problems and parallel matrix computations, expanded treatment of CS decomposition, an updated overview of floating point arithmetic, a more accurate rendition of the modified Gram-Schmidt process, and new material devoted to GMRES, QMR, and other methods designed to handle the sparse unsymmetric linear system problem.


Book Synopsis Matrix Computations by : Gene H. Golub

Download or read book Matrix Computations written by Gene H. Golub and published by JHU Press. This book was released on 1996-10-15 with total page 734 pages. Available in PDF, EPUB and Kindle. Book excerpt: Revised and updated, the third edition of Golub and Van Loan's classic text in computer science provides essential information about the mathematical background and algorithmic skills required for the production of numerical software. This new edition includes thoroughly revised chapters on matrix multiplication problems and parallel matrix computations, expanded treatment of CS decomposition, an updated overview of floating point arithmetic, a more accurate rendition of the modified Gram-Schmidt process, and new material devoted to GMRES, QMR, and other methods designed to handle the sparse unsymmetric linear system problem.


Numerical Linear Algebra for High-performance Computers

Numerical Linear Algebra for High-performance Computers

Author: Jack J. Dongarra

Publisher: SIAM

Published: 1998-01-01

Total Pages: 360

ISBN-13: 9780898719611

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This book presents a unified treatment of recently developed techniques and current understanding about solving systems of linear equations and large scale eigenvalue problems on high-performance computers. It provides a rapid introduction to the world of vector and parallel processing for these linear algebra applications. Topics include major elements of advanced-architecture computers and their performance, recent algorithmic development, and software for direct solution of dense matrix problems, direct solution of sparse systems of equations, iterative solution of sparse systems of equations, and solution of large sparse eigenvalue problems.


Book Synopsis Numerical Linear Algebra for High-performance Computers by : Jack J. Dongarra

Download or read book Numerical Linear Algebra for High-performance Computers written by Jack J. Dongarra and published by SIAM. This book was released on 1998-01-01 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a unified treatment of recently developed techniques and current understanding about solving systems of linear equations and large scale eigenvalue problems on high-performance computers. It provides a rapid introduction to the world of vector and parallel processing for these linear algebra applications. Topics include major elements of advanced-architecture computers and their performance, recent algorithmic development, and software for direct solution of dense matrix problems, direct solution of sparse systems of equations, iterative solution of sparse systems of equations, and solution of large sparse eigenvalue problems.


Parallel Algorithms for Matrix Computations

Parallel Algorithms for Matrix Computations

Author: K. Gallivan

Publisher: SIAM

Published: 1990-01-01

Total Pages: 207

ISBN-13: 9781611971705

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Describes a selection of important parallel algorithms for matrix computations. Reviews the current status and provides an overall perspective of parallel algorithms for solving problems arising in the major areas of numerical linear algebra, including (1) direct solution of dense, structured, or sparse linear systems, (2) dense or structured least squares computations, (3) dense or structured eigenvaluen and singular value computations, and (4) rapid elliptic solvers. The book emphasizes computational primitives whose efficient execution on parallel and vector computers is essential to obtain high performance algorithms. Consists of two comprehensive survey papers on important parallel algorithms for solving problems arising in the major areas of numerical linear algebra--direct solution of linear systems, least squares computations, eigenvalue and singular value computations, and rapid elliptic solvers, plus an extensive up-to-date bibliography (2,000 items) on related research.


Book Synopsis Parallel Algorithms for Matrix Computations by : K. Gallivan

Download or read book Parallel Algorithms for Matrix Computations written by K. Gallivan and published by SIAM. This book was released on 1990-01-01 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes a selection of important parallel algorithms for matrix computations. Reviews the current status and provides an overall perspective of parallel algorithms for solving problems arising in the major areas of numerical linear algebra, including (1) direct solution of dense, structured, or sparse linear systems, (2) dense or structured least squares computations, (3) dense or structured eigenvaluen and singular value computations, and (4) rapid elliptic solvers. The book emphasizes computational primitives whose efficient execution on parallel and vector computers is essential to obtain high performance algorithms. Consists of two comprehensive survey papers on important parallel algorithms for solving problems arising in the major areas of numerical linear algebra--direct solution of linear systems, least squares computations, eigenvalue and singular value computations, and rapid elliptic solvers, plus an extensive up-to-date bibliography (2,000 items) on related research.


Iterative Methods for Sparse Linear Systems

Iterative Methods for Sparse Linear Systems

Author: Yousef Saad

Publisher: SIAM

Published: 2003-04-01

Total Pages: 537

ISBN-13: 0898715342

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Mathematics of Computing -- General.


Book Synopsis Iterative Methods for Sparse Linear Systems by : Yousef Saad

Download or read book Iterative Methods for Sparse Linear Systems written by Yousef Saad and published by SIAM. This book was released on 2003-04-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.


Numerical Solution of Integral Equations

Numerical Solution of Integral Equations

Author: Michael A. Golberg

Publisher: Springer Science & Business Media

Published: 2013-11-11

Total Pages: 428

ISBN-13: 1489925937

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In 1979, I edited Volume 18 in this series: Solution Methods for Integral Equations: Theory and Applications. Since that time, there has been an explosive growth in all aspects of the numerical solution of integral equations. By my estimate over 2000 papers on this subject have been published in the last decade, and more than 60 books on theory and applications have appeared. In particular, as can be seen in many of the chapters in this book, integral equation techniques are playing an increas ingly important role in the solution of many scientific and engineering problems. For instance, the boundary element method discussed by Atkinson in Chapter 1 is becoming an equal partner with finite element and finite difference techniques for solving many types of partial differential equations. Obviously, in one volume it would be impossible to present a complete picture of what has taken place in this area during the past ten years. Consequently, we have chosen a number of subjects in which significant advances have been made that we feel have not been covered in depth in other books. For instance, ten years ago the theory of the numerical solution of Cauchy singular equations was in its infancy. Today, as shown by Golberg and Elliott in Chapters 5 and 6, the theory of polynomial approximations is essentially complete, although many details of practical implementation remain to be worked out.


Book Synopsis Numerical Solution of Integral Equations by : Michael A. Golberg

Download or read book Numerical Solution of Integral Equations written by Michael A. Golberg and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1979, I edited Volume 18 in this series: Solution Methods for Integral Equations: Theory and Applications. Since that time, there has been an explosive growth in all aspects of the numerical solution of integral equations. By my estimate over 2000 papers on this subject have been published in the last decade, and more than 60 books on theory and applications have appeared. In particular, as can be seen in many of the chapters in this book, integral equation techniques are playing an increas ingly important role in the solution of many scientific and engineering problems. For instance, the boundary element method discussed by Atkinson in Chapter 1 is becoming an equal partner with finite element and finite difference techniques for solving many types of partial differential equations. Obviously, in one volume it would be impossible to present a complete picture of what has taken place in this area during the past ten years. Consequently, we have chosen a number of subjects in which significant advances have been made that we feel have not been covered in depth in other books. For instance, ten years ago the theory of the numerical solution of Cauchy singular equations was in its infancy. Today, as shown by Golberg and Elliott in Chapters 5 and 6, the theory of polynomial approximations is essentially complete, although many details of practical implementation remain to be worked out.


A Survey of Preconditioned Iterative Methods

A Survey of Preconditioned Iterative Methods

Author: Are Magnus Bruaset

Publisher: Routledge

Published: 2018-12-13

Total Pages: 175

ISBN-13: 1351469371

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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


Book Synopsis A Survey of Preconditioned Iterative Methods by : Are Magnus Bruaset

Download or read book A Survey of Preconditioned Iterative Methods written by Are Magnus Bruaset and published by Routledge. This book was released on 2018-12-13 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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