The Shifted Hessenberg System Solve Computation
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The Shifted Hessenberg System Solve Computation
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Author : Greg Henry
language : en
Publisher:
Release Date : 1994
The Shifted Hessenberg System Solve Computation written by Greg Henry and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Algebras, Linear categories.
Parallelism In Matrix Computations
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Author : Efstratios Gallopoulos
language : en
Publisher: Springer
Release Date : 2015-07-25
Parallelism In Matrix Computations written by Efstratios Gallopoulos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-25 with Technology & Engineering categories.
This book is primarily intended as a research monograph that could also be used in graduate courses for the design of parallel algorithms in matrix computations. It assumes general but not extensive knowledge of numerical linear algebra, parallel architectures, and parallel programming paradigms. The book consists of four parts: (I) Basics; (II) Dense and Special Matrix Computations; (III) Sparse Matrix Computations; and (IV) Matrix functions and characteristics. Part I deals with parallel programming paradigms and fundamental kernels, including reordering schemes for sparse matrices. Part II is devoted to dense matrix computations such as parallel algorithms for solving linear systems, linear least squares, the symmetric algebraic eigenvalue problem, and the singular-value decomposition. It also deals with the development of parallel algorithms for special linear systems such as banded ,Vandermonde ,Toeplitz ,and block Toeplitz systems. Part III addresses sparse matrix computations: (a) the development of parallel iterative linear system solvers with emphasis on scalable preconditioners, (b) parallel schemes for obtaining a few of the extreme eigenpairs or those contained in a given interval in the spectrum of a standard or generalized symmetric eigenvalue problem, and (c) parallel methods for computing a few of the extreme singular triplets. Part IV focuses on the development of parallel algorithms for matrix functions and special characteristics such as the matrix pseudospectrum and the determinant. The book also reviews the theoretical and practical background necessary when designing these algorithms and includes an extensive bibliography that will be useful to researchers and students alike. The book brings together many existing algorithms for the fundamental matrix computations that have a proven track record of efficient implementation in terms of data locality and data transfer on state-of-the-art systems, as well as several algorithms that are presented for the first time, focusing on the opportunities for parallelism and algorithm robustness.
Proceedings Of The Seventh Siam Conference On Parallel Processing For Scientific Computing
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Author : David H. Bailey
language : en
Publisher: SIAM
Release Date : 1995-01-01
Proceedings Of The Seventh Siam Conference On Parallel Processing For Scientific Computing written by David H. Bailey and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-01 with Science categories.
Proceedings -- Parallel Computing.
Calculation Of Pseudospectra By The Arnoldi Iteration
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Author : Kim Chuan Toh
language : en
Publisher:
Release Date : 1994
Calculation Of Pseudospectra By The Arnoldi Iteration written by Kim Chuan Toh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Hydrodynamics categories.
Krylov Methods For Nonsymmetric Linear Systems
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Author : Gérard Meurant
language : en
Publisher: Springer Nature
Release Date : 2020-10-02
Krylov Methods For Nonsymmetric Linear Systems written by Gérard Meurant and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-02 with Mathematics categories.
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.
Improving Data Re Use In Eigenvalue Related Computations
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Author : Greg Henry
language : en
Publisher:
Release Date : 1994
Improving Data Re Use In Eigenvalue Related Computations written by Greg Henry and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.
Numerical Linear Algebra With Applications
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Author : William Ford
language : en
Publisher: Academic Press
Release Date : 2025-06-10
Numerical Linear Algebra With Applications written by William Ford and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-10 with Mathematics categories.
Numerical Linear Algebra with Applications: Using MATLAB and Octave, Second Edition provides practical knowledge on modern computational techniques for the numerical solution of linear algebra problems. The book offers a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions. Useful to readers regardless of background, the text begins with six introductory courses to provide background for those who haven't taken applied or theoretical linear algebra. This approach offers a thorough explanation of the issues and methods for practical computing using MATLAB as the vehicle for computation.Appropriate for advanced undergraduate and early graduate courses on numerical linear algebra, this useful textbook explores numerous applications to engineering and science. - Features six introductory chapters to provide the required background for readers without coursework in applied or theoretical linear algebra - Offers a through discussion of the algorithms necessary for the accurate computation of the solution to the most frequently occurring problems in numerical linear algebra - Provides illustrative examples from engineering and science applications - Includes online teaching support for qualified instructors (Solutions Manual, PowerPoint Slides) and study materials for students (Text examples, Algorithms)
Introduction To Matrix Computations
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Author : G. W. Stewart
language : en
Publisher: Elsevier
Release Date : 1973-06-15
Introduction To Matrix Computations written by G. W. Stewart and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973-06-15 with Mathematics categories.
Numerical linear algebra is far too broad a subject to treat in a single introductory volume. Stewart has chosen to treat algorithms for solving linear systems, linear least squares problems, and eigenvalue problems involving matrices whose elements can all be contained in the high-speed storage of a computer. By way of theory, the author has chosen to discuss the theory of norms and perturbation theory for linear systems and for the algebraic eigenvalue problem. These choices exclude, among other things, the solution of large sparse linear systems by direct and iterative methods, linear programming, and the useful Perron-Frobenious theory and its extensions. However, a person who has fully mastered the material in this book should be well prepared for independent study in other areas of numerical linear algebra.
Numerical Methods For Structured Markov Chains
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Author : Dario A. Bini
language : en
Publisher: OUP Oxford
Release Date : 2005-02-03
Numerical Methods For Structured Markov Chains written by Dario A. Bini and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-03 with Mathematics categories.
Intersecting two large research areas - numerical analysis and applied probability/queuing theory - this book is a self-contained introduction to the numerical solution of structured Markov chains, which have a wide applicability in queuing theory and stochastic modeling and include M/G/1 and GI/M/1-type Markov chain, quasi-birth-death processes, non-skip free queues and tree-like stochastic processes. Written for applied probabilists and numerical analysts, but accessible to engineers and scientists working on telecommunications and evaluation of computer systems performances, it provides a systematic treatment of the theory and algorithms for important families of structured Markov chains and a thorough overview of the current literature. The book, consisting of nine Chapters, is presented in three parts. Part 1 covers a basic description of the fundamental concepts related to Markov chains, a systematic treatment of the structure matrix tools, including finite Toeplitz matrices, displacement operators, FFT, and the infinite block Toeplitz matrices, their relationship with matrix power series and the fundamental problems of solving matrix equations and computing canonical factorizations. Part 2 deals with the description and analysis of structure Markov chains and includes M/G/1, quasi-birth-death processes, non-skip-free queues and tree-like processes. Part 3 covers solution algorithms where new convergence and applicability results are proved. Each chapter ends with bibliographic notes for further reading, and the book ends with an appendix collecting the main general concepts and results used in the book, a list of the main annotations and algorithms used in the book, and an extensive index.
Numerical Methods For General And Structured Eigenvalue Problems
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Author : Daniel Kressner
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-20
Numerical Methods For General And Structured Eigenvalue Problems written by Daniel Kressner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-20 with Mathematics categories.
This book is about computing eigenvalues, eigenvectors, and invariant subspaces of matrices. Treatment includes generalized and structured eigenvalue problems and all vital aspects of eigenvalue computations. A unique feature is the detailed treatment of structured eigenvalue problems, providing insight on accuracy and efficiency gains to be expected from algorithms that take the structure of a matrix into account.