Download or read book Direct Methods for Sparse Matrices written by I. S. Duff and published by Oxford University Press. This book was released on 2017-02-10 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of sparse matrices has its root in such diverse fields as management science, power systems analysis, surveying, circuit theory, and structural analysis. Efficient use of sparsity is a key to solving large problems in many fields. This second edition is a complete rewrite of the first edition published 30 years ago. Much has changed since that time. Problems have grown greatly in size and complexity; nearly all examples in the first edition were of order less than 5,000 in the first edition, and are often more than a million in the second edition. Computer architectures are now much more complex, requiring new ways of adapting algorithms to parallel environments with memory hierarchies. Because the area is such an important one to all of computational science and engineering, a huge amount of research has been done in the last 30 years, some of it by the authors themselves. This new research is integrated into the text with a clear explanation of the underlying mathematics and algorithms. New research that is described includes new techniques for scaling and error control, new orderings, new combinatorial techniques for partitioning both symmetric and unsymmetric problems, and a detailed description of the multifrontal approach to solving systems that was pioneered by the research of the authors and colleagues. This includes a discussion of techniques for exploiting parallel architectures and new work for indefinite and unsymmetric systems.
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 Preconditioned Conjugate Gradient Methods written by Owe Axelsson and published by Springer. This book was released on 2006-11-14 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 180 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
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 Krylov Methods for Nonsymmetric Linear Systems written by Gérard Meurant and published by Springer Nature. This book was released on 2020-10-02 with total page 686 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematical Programming The State of the Art written by A. Bachem and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the late forties, Mathematical Programming became a scientific discipline in its own right. Since then it has experienced a tremendous growth. Beginning with economic and military applications, it is now among the most important fields of applied mathematics with extensive use in engineering, natural sciences, economics, and biological sciences. The lively activity in this area is demonstrated by the fact that as early as 1949 the first "Symposium on Mathe matical Programming" took place in Chicago. Since then mathematical programmers from all over the world have gath ered at the intfrnational symposia of the Mathematical Programming Society roughly every three years to present their recent research, to exchange ideas with their colleagues and to learn about the latest developments in their own and related fields. In 1982, the XI. International Symposium on Mathematical Programming was held at the University of Bonn, W. Germany, from August 23 to 27. It was organized by the Institut fUr Okonometrie und Operations Re search of the University of Bonn in collaboration with the Sonderforschungs bereich 21 of the Deutsche Forschungsgemeinschaft. This volume constitutes part of the outgrowth of this symposium and docu ments its scientific activities. Part I of the book contains information about the symposium, welcoming addresses, lists of committees and sponsors and a brief review about the Ful kerson Prize and the Dantzig Prize which were awarded during the opening ceremony.
Download or read book A Multigrid Tutorial written by William L. Briggs and published by SIAM. This book was released on 2000-07-01 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Download or read book Nonlinear Programming written by Mordecai Avriel and published by Courier Corporation. This book was released on 2003-01-01 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: This overview provides a single-volume treatment of key algorithms and theories. Begins with the derivation of optimality conditions and discussions of convex programming, duality, generalized convexity, and analysis of selected nonlinear programs, and then explores techniques for numerical solutions and unconstrained optimization methods. 1976 edition. Includes 58 figures and 7 tables.
Download or read book Linear and Nonlinear Conjugate Gradient related Methods written by Loyce M. Adams and published by SIAM. This book was released on 1996-01-01 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the AMS-IMS-SIAM Summer Research Conference held at the University of Washington, July 1995.
Download or read book Krylov Subspace Methods for Linear Systems written by Tomohiro Sogabe and published by Springer Nature. This book was released on 2023-01-20 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on Krylov subspace methods for solving linear systems, which are known as one of the top 10 algorithms in the twentieth century, such as Fast Fourier Transform and Quick Sort (SIAM News, 2000). Theoretical aspects of Krylov subspace methods developed in the twentieth century are explained and derived in a concise and unified way. Furthermore, some Krylov subspace methods in the twenty-first century are described in detail, such as the COCR method for complex symmetric linear systems, the BiCR method, and the IDR(s) method for non-Hermitian linear systems. The strength of the book is not only in describing principles of Krylov subspace methods but in providing a variety of applications: shifted linear systems and matrix functions from the theoretical point of view, as well as partial differential equations, computational physics, computational particle physics, optimizations, and machine learning from a practical point of view. The book is self-contained in that basic necessary concepts of numerical linear algebra are explained, making it suitable for senior undergraduates, postgraduates, and researchers in mathematics, engineering, and computational science. Readers will find it a useful resource for understanding the principles and properties of Krylov subspace methods and correctly using those methods for solving problems in the future.
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 343 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 ofthe block conjugate-gradient algorithm and it is this observation thatpermits the unification of the theory. The two major sub-classes of thosemethods, the Lanczos and the Hestenes-Stiefel, are developed in parallel asnatural generalisations of the Orthodir (GCR) and Orthomin algorithms. Theseare themselves based on Arnoldi's algorithm and a generalised Gram-Schmidtalgorithm and their properties, in particular their stability properties,are determined by the two matrices that define the block conjugate-gradientalgorithm. These are the matrix of coefficients and the preconditioningmatrix.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 Parallel Numerical Algorithms written by David E. Keyes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Applied Iterative Methods written by Louis A. Hageman and published by Elsevier. This book was released on 2014-06-28 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applied Iterative Methods
Download or read book The Lanczos and Conjugate Gradient Algorithms written by Gerard Meurant and published by SIAM. This book was released on 2006-08-01 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most comprehensive and up-to-date discussion available of the Lanczos and CG methods for computing eigenvalues and solving linear systems.
Download or read book Linear Algebra in Signals Systems and Control written by Biswa Nath Datta and published by SIAM. This book was released on 1988-01-01 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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