Download or read book Computer Solution of Large Linear Systems written by Gerard Meurant and published by Elsevier. This book was released on 1999-06-16 with total page 777 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with numerical methods for solving large sparse linear systems of equations, particularly those arising from the discretization of partial differential equations. It covers both direct and iterative methods. Direct methods which are considered are variants of Gaussian elimination and fast solvers for separable partial differential equations in rectangular domains. The book reviews the classical iterative methods like Jacobi, Gauss-Seidel and alternating directions algorithms. A particular emphasis is put on the conjugate gradient as well as conjugate gradient -like methods for non symmetric problems. Most efficient preconditioners used to speed up convergence are studied. A chapter is devoted to the multigrid method and the book ends with domain decomposition algorithms that are well suited for solving linear systems on parallel computers.
Download or read book Computer solution of large linear systems written by Gérard A. Meurant and published by . This book was released on 1999 with total page 753 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Iterative Solution of Large Linear Systems written by David M. Young and published by Elsevier. This book was released on 2014-05-10 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: Iterative Solution of Large Linear Systems describes the systematic development of a substantial portion of the theory of iterative methods for solving large linear systems, with emphasis on practical techniques. The focal point of the book is an analysis of the convergence properties of the successive overrelaxation (SOR) method as applied to a linear system where the matrix is "consistently ordered". Comprised of 18 chapters, this volume begins by showing how the solution of a certain partial differential equation by finite difference methods leads to a large linear system with a sparse matrix. The next chapter reviews matrix theory and the properties of matrices, as well as several theorems of matrix theory without proof. A number of iterative methods, including the SOR method, are then considered. Convergence theorems are also given for various iterative methods under certain assumptions on the matrix A of the system. Subsequent chapters deal with the eigenvalues of the SOR method for consistently ordered matrices; the optimum relaxation factor; nonstationary linear iterative methods; and semi-iterative methods. This book will be of interest to students and practitioners in the fields of computer science and applied mathematics.
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.
Download or read book Computer Solution of Large Sparse Positive Definite Systems written by Alan George and published by Prentice Hall. This book was released on 1981 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 1988-04-30 with total page 330 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.
Download or read book Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications written by Daniele Bertaccini and published by CRC Press. This book was released on 2018-02-19 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Direct Methods for Sparse Linear Systems written by Timothy A. Davis and published by SIAM. This book was released on 2006-09-01 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The sparse backslash book. Everything you wanted to know but never dared to ask about modern direct linear solvers. Chen Greif, Assistant Professor, Department of Computer Science, University of British Columbia.Overall, the book is magnificent. It fills a long-felt need for an accessible textbook on modern sparse direct methods. Its choice of scope is excellent John Gilbert, Professor, Department of Computer Science, University of California, Santa Barbara.Computational scientists often encounter problems requiring the solution of sparse systems of linear equations. Attacking these problems efficiently requires an in-depth knowledge of the underlying theory, algorithms, and data structures found in sparse matrix software libraries. Here, Davis presents the fundamentals of sparse matrix algorithms to provide the requisite background. The book includes CSparse, a concise downloadable sparse matrix package that illustrates the algorithms and theorems presented in the book and equips readers with the tools necessary to understand larger and more complex software packages.With a strong emphasis on MATLAB and the C programming language, Direct Methods for Sparse Linear Systems equips readers with the working knowledge required to use sparse solver packages and write code to interface applications to those packages. The book also explains how MATLAB performs its sparse matrix computations.Audience This invaluable book is essential to computational scientists and software developers who want to understand the theory and algorithms behind modern techniques used to solve large sparse linear systems. The book also serves as an excellent practical resource for students with an interest in combinatorial scientific computing.Preface; Chapter 1: Introduction; Chapter 2: Basic algorithms; Chapter 3: Solving triangular systems; Chapter 4: Cholesky factorization; Chapter 5: Orthogonal methods; Chapter 6: LU factorization; Chapter 7: Fill-reducing orderings; Chapter 8: Solving sparse linear systems; Chapter 9: CSparse; Chapter 10: Sparse matrices in MATLAB; Appendix: Basics of the C programming language; Bibliography; Index.
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.
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
Download or read book Templates for the Solution of Linear Systems written by Richard Barrett and published by SIAM. This book was released on 1994-01-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Advances in Cryptology CRYPTO 90 written by Alfred J. Menezes and published by Springer. This book was released on 2003-06-30 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: Crypto '90 marked the tenth anniversary of the Crypto conferences held at the University of California at Santa Barbara. The conference was held from August 11 to August 15, 1990 and was sponsored by the International Association for Cryptologic Research, in cooperation with the IEEE Computer Society Technical Committee on Security and Privacy and the Department of Computer Science of the University of California at Santa Barbara. 227 participants from twenty countries around the world. Crypto '90 attracted Roughly 35% of attendees were from academia, 45% from industry and 20% from government. The program was intended to provide a balance between the purely theoretical and the purely practical aspects of cryptography to meet the needs and diversified interests of these various groups. The overall organization of the conference was superbly handled by the general chairperson Sherry McMahan. All of the outstanding features of Crypto, which we have come to expect over the years, were again present and, in addition to all of this, she did a magnificent job in the preparation of the book of abstracts. This is a crucial part of the program and we owe her a great deal of thanks.
Download or read book Krylov Solvers for Linear Algebraic Systems written by Charles George Broyden and published by Elsevier. This book was released on 2004-09-08 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first four chapters of this book give a comprehensive and unified theory of the Krylov methods. Many of these are shown to be particular examples of the block conjugate-gradient algorithm and it is this observation that permits the unification of the theory. The two major sub-classes of those methods, the Lanczos and the Hestenes-Stiefel, are developed in parallel as natural generalisations of the Orthodir (GCR) and Orthomin algorithms. These are themselves based on Arnoldi's algorithm and a generalised Gram-Schmidt algorithm and their properties, in particular their stability properties, are determined by the two matrices that define the block conjugate-gradient algorithm. These are the matrix of coefficients and the preconditioning matrix. In Chapter 5 the"transpose-free" algorithms based on the conjugate-gradient squared algorithm are presented while Chapter 6 examines the various ways in which the QMR technique has been exploited. Look-ahead methods and general block methods are dealt with in Chapters 7 and 8 while Chapter 9 is devoted to error analysis of two basic algorithms. In Chapter 10 the results of numerical testing of the more important algorithms in their basic forms (i.e. without look-ahead or preconditioning) are presented and these are related to the structure of the algorithms and the general theory. Graphs illustrating the performances of various algorithm/problem combinations are given via a CD-ROM. Chapter 11, by far the longest, gives a survey of preconditioning techniques. These range from the old idea of polynomial preconditioning via SOR and ILU preconditioning to methods like SpAI, AInv and the multigrid methods that were developed specifically for use with parallel computers. Chapter 12 is devoted to dual algorithms like Orthores and the reverse algorithms of Hegedus. Finally certain ancillary matters like reduction to Hessenberg form, Chebychev polynomials and the companion matrix are described in a series of appendices. · comprehensive and unified approach · up-to-date chapter on preconditioners · complete theory of stability · includes dual and reverse methods · comparison of algorithms on CD-ROM · objective assessment of algorithms
Download or read book Numerical Modeling for Electromagnetic Non Destructive Evaluation written by N. Ida and published by Springer Science & Business Media. This book was released on 1994-12-31 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text on numerical methods applied to the analysis of electromagnetic nondestructive testing (NOT) phenomena is the first in a series devoted to all aspects of engineering nondestructive evaluation. The timing of this series is most appropriate as many university engineering/physics faculties around the world, recognizing the industrial significance of the subject, are organizing new courses and programs with engineering NOE as a theme. Additional texts in the series will cover electromagnetics for engineering NOE, microwave NOT methods, ultrasonic testing, radiographic methods and signal processing for NOE. It is the intended purpose of the series to provide senior-graduate level coverage of the material suitable for university curricula and to be generally useful to those in industry with engineering degrees who wish to upgrade their NOE skills beyond those needed for certification. This dual purpose for the series reflects the very applied nature of NOE and the need to develop suitable texts capable of bridging the gap between research laboratory studies of NOE phenomena and the real world of certification and industrial applications. The reader might be tempted to question these assertions in light of the rather mathematical nature of this first text. However, the subject of numerical modeling is of critical importance to a thorough understanding of the field-defect interactions at the heart of all electromagnetic NOT phenomena.
Download or read book Algorithms for Sparse Linear Systems written by Jennifer Scott and published by Springer Nature. This book was released on 2023-04-29 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Numerical Analysis Historical Developments in the 20th Century written by C. Brezinski and published by Elsevier. This book was released on 2012-12-02 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical analysis has witnessed many significant developments in the 20th century. This book brings together 16 papers dealing with historical developments, survey papers and papers on recent trends in selected areas of numerical analysis, such as: approximation and interpolation, solution of linear systems and eigenvalue problems, iterative methods, quadrature rules, solution of ordinary-, partial- and integral equations. The papers are reprinted from the 7-volume project of the Journal of Computational and Applied Mathematics on '/homepage/sac/cam/na2000/index.htmlNumerical Analysis 2000'. An introductory survey paper deals with the history of the first courses on numerical analysis in several countries and with the landmarks in the development of important algorithms and concepts in the field.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1987 with total page 1126 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
