Download or read book Gmres a Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems written by Yale University. Department of Computer Science and published by . This book was released on 1982 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book MGMRES written by and published by . This book was released on 1996 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is concerned with the solution of the linear system Au = b, where A is a real square nonsingular matrix which is large, sparse and nonsymmetric. We consider the use of Krylov subspace methods. We first choose an initial approximation u{sup (0)} to the solution {bar u} = A−1b. The GMRES (Generalized Minimum Residual Algorithm for Solving Non Symmetric Linear Systems) method was developed by Saad and Schultz (1986) and used extensively for many years, for sparse systems. This paper considers a generalization of GMRES; it is similar to GMRES except that we let Z = A{sup T}Y, where Y is a nonsingular matrix which is symmetric but not necessarily SPD.
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 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 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 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 Matrix Polynomials written by I. Gohberg and published by SIAM. This book was released on 2009-07-23 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the definitive treatment of the theory of polynomials in a complex variable with matrix coefficients. Basic matrix theory can be viewed as the study of the special case of polynomials of first degree; the theory developed in Matrix Polynomials is a natural extension of this case to polynomials of higher degree. It has applications in many areas, such as differential equations, systems theory, the Wiener-Hopf technique, mechanics and vibrations, and numerical analysis. Although there have been significant advances in some quarters, this work remains the only systematic development of the theory of matrix polynomials. The book is appropriate for students, instructors, and researchers in linear algebra, operator theory, differential equations, systems theory, and numerical analysis. Its contents are accessible to readers who have had undergraduate-level courses in linear algebra and complex analysis.
Download or read book Numerical Methods for Least Squares Problems written by Ake Bjorck and published by SIAM. This book was released on 1996-01-01 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: The method of least squares was discovered by Gauss in 1795. It has since become the principal tool to reduce the influence of errors when fitting models to given observations. Today, applications of least squares arise in a great number of scientific areas, such as statistics, geodetics, signal processing, and control. In the last 20 years there has been a great increase in the capacity for automatic data capturing and computing. Least squares problems of large size are now routinely solved. Tremendous progress has been made in numerical methods for least squares problems, in particular for generalized and modified least squares problems and direct and iterative methods for sparse problems. Until now there has not been a monograph that covers the full spectrum of relevant problems and methods in least squares. This volume gives an in-depth treatment of topics such as methods for sparse least squares problems, iterative methods, modified least squares, weighted problems, and constrained and regularized problems. The more than 800 references provide a comprehensive survey of the available literature on the subject.
Download or read book Allgemeiner Teil Deutsch written by Bremen Senator für Bildung, Wissenschaft und Kunst and published by . This book was released on 1977 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Matrix Computations written by Gene Howard Golub and published by . This book was released on 1983 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Solving Linear Systems on Vector and Shared Memory Computers written by J. J. Dongarra and published by Society for Industrial and Applied Mathematics (SIAM). This book was released on 1991 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Parallelism.
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 Qualitative Computing written by Françoise Chatelin and published by World Scientific. This book was released on 2012 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Qualitative Computing; Hypercomputation in Dickson Algebras; Scales of Complexity and Linear Reachability; Singular Values for the Multiplication Maps; Computation Beyond Classical Logic; Complexification of the Arithmetic; Homotopic Deviation in Linear Algebra; The Discrete and the Continuous; Arithmetic in the Alternative Dickson Division Algebras; The Real and the Complex.
Download or read book A Brief Introduction to Numerical Analysis written by Eugene E. Tyrtyshnikov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: A logically organized advanced textbook, which turns the reader into an active participant by asking questions, hinting, giving direct recommendations, comparing different methods, and discussing "pessimistic" and "optimistic" approaches to numerical analysis. Advanced students and graduate students majoring in computer science, physics and mathematics will find this book helpful.
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 Iterative Methods for Solving Linear Systems written by Anne Greenbaum and published by SIAM. This book was released on 1997-01-01 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Download or read book Iterative Methods for Linear and Nonlinear Equations written by C. T. Kelley and published by SIAM. This book was released on 1995-01-01 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear and nonlinear systems of equations are the basis for many, if not most, of the models of phenomena in science and engineering, and their efficient numerical solution is critical to progress in these areas. This is the first book to be published on nonlinear equations since the mid-1980s. Although it stresses recent developments in this area, such as Newton-Krylov methods, considerable material on linear equations has been incorporated. This book focuses on a small number of methods and treats them in depth. The author provides a complete analysis of the conjugate gradient and generalized minimum residual iterations as well as recent advances including Newton-Krylov methods, incorporation of inexactness and noise into the analysis, new proofs and implementations of Broyden's method, and globalization of inexact Newton methods. Examples, methods, and algorithmic choices are based on applications to infinite dimensional problems such as partial differential equations and integral equations. The analysis and proof techniques are constructed with the infinite dimensional setting in mind and the computational examples and exercises are based on the MATLAB environment.
