Matrix Algorithms
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Matrix Algorithms
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Author : G. W. Stewart
language : en
Publisher: SIAM
Release Date : 1998-08-01
Matrix Algorithms written by G. W. Stewart and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-08-01 with Mathematics categories.
This volume is the first in a self-contained five-volume series devoted to matrix algorithms. It focuses on the computation of matrix decompositions--that is, the factorization of matrices into products of similar ones. The first two chapters provide the required background from mathematics and computer science needed to work effectively in matrix computations. The remaining chapters are devoted to the LU and QR decompositions--their computation and applications. The singular value decomposition is also treated, although algorithms for its computation will appear in the second volume of the series. The present volume contains 65 algorithms formally presented in pseudocode. Other volumes in the series will treat eigensystems, iterative methods, sparse matrices, and structured problems. The series is aimed at the nonspecialist who needs more than black-box proficiency with matrix computations. To give the series focus, the emphasis is on algorithms, their derivation, and their analysis. The reader is assumed to have a knowledge of elementary analysis and linear algebra and a reasonable amount of programming experience, typically that of the beginning graduate engineer or the undergraduate in an honors program. Strictly speaking, the individual volumes are not textbooks, although they are intended to teach, the guiding principle being that if something is worth explaining, it is worth explaining fully. This has necessarily restricted the scope of the series, but the selection of topics should give the reader a sound basis for further study.
Matrix Algorithms In Matlab
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Author : Ong U. Routh
language : en
Publisher: Academic Press
Release Date : 2016-04-22
Matrix Algorithms In Matlab written by Ong U. Routh and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-22 with Computers categories.
Matrix Algorithms in MATLAB focuses on the MATLAB code implementations of matrix algorithms. The MATLAB codes presented in the book are tested with thousands of runs of MATLAB randomly generated matrices, and the notation in the book follows the MATLAB style to ensure a smooth transition from formulation to the code, with MATLAB codes discussed in this book kept to within 100 lines for the sake of clarity. The book provides an overview and classification of the interrelations of various algorithms, as well as numerous examples to demonstrate code usage and the properties of the presented algorithms. Despite the wide availability of computer programs for matrix computations, it continues to be an active area of research and development. New applications, new algorithms, and improvements to old algorithms are constantly emerging. Presents the first book available on matrix algorithms implemented in real computer code Provides algorithms covered in three parts, the mathematical development of the algorithm using a simple example, the code implementation, and then numerical examples using the code Allows readers to gain a quick understanding of an algorithm by debugging or reading the source code Includes downloadable codes on an accompanying companion website, www.matrixalgorithmsinmatlab.com, that can be used in other software development
Matrix Algorithms
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Author : G. W. Stewart
language : en
Publisher: SIAM
Release Date : 2001-08-30
Matrix Algorithms written by G. W. Stewart and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-08-30 with Mathematics categories.
This is the second volume in a projected five-volume survey of numerical linear algebra and matrix algorithms. It treats the numerical solution of dense and large-scale eigenvalue problems with an emphasis on algorithms and the theoretical background required to understand them. The notes and reference sections contain pointers to other methods along with historical comments. The book is divided into two parts: dense eigenproblems and large eigenproblems. The first part gives a full treatment of the widely used QR algorithm, which is then applied to the solution of generalized eigenproblems and the computation of the singular value decomposition. The second part treats Krylov sequence methods such as the Lanczos and Arnoldi algorithms and presents a new treatment of the Jacobi-Davidson method. These volumes are not intended to be encyclopedic, but provide the reader with the theoretical and practical background to read the research literature and implement or modify new algorithms.
Polynomial And Matrix Computations
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Author : Dario Bini
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Polynomial And Matrix Computations written by Dario Bini 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 2012-12-06 with Computers categories.
Our Subjects and Objectives. This book is about algebraic and symbolic computation and numerical computing (with matrices and polynomials). It greatly extends the study of these topics presented in the celebrated books of the seventies, [AHU] and [BM] (these topics have been under-represented in [CLR], which is a highly successful extension and updating of [AHU] otherwise). Compared to [AHU] and [BM] our volume adds extensive material on parallel com putations with general matrices and polynomials, on the bit-complexity of arithmetic computations (including some recent techniques of data compres sion and the study of numerical approximation properties of polynomial and matrix algorithms), and on computations with Toeplitz matrices and other dense structured matrices. The latter subject should attract people working in numerous areas of application (in particular, coding, signal processing, control, algebraic computing and partial differential equations). The au thors' teaching experience at the Graduate Center of the City University of New York and at the University of Pisa suggests that the book may serve as a text for advanced graduate students in mathematics and computer science who have some knowledge of algorithm design and wish to enter the exciting area of algebraic and numerical computing. The potential readership may also include algorithm and software designers and researchers specializing in the design and analysis of algorithms, computational complexity, alge braic and symbolic computing, and numerical computation.
Matrix Algorithms
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Author : G. W. Stewart
language : en
Publisher: SIAM
Release Date : 1998-08-01
Matrix Algorithms written by G. W. Stewart and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-08-01 with Mathematics categories.
This volume is the first in a self-contained five-volume series devoted to matrix algorithms. It focuses on the computation of matrix decompositions--that is, the factorization of matrices into products of similar ones. The first two chapters provide the required background from mathematics and computer science needed to work effectively in matrix computations. The remaining chapters are devoted to the LU and QR decompositions--their computation and applications. The singular value decomposition is also treated, although algorithms for its computation will appear in the second volume of the series. The present volume contains 65 algorithms formally presented in pseudocode. Other volumes in the series will treat eigensystems, iterative methods, sparse matrices, and structured problems. The series is aimed at the nonspecialist who needs more than black-box proficiency with matrix computations. To give the series focus, the emphasis is on algorithms, their derivation, and their analysis. The reader is assumed to have a knowledge of elementary analysis and linear algebra and a reasonable amount of programming experience, typically that of the beginning graduate engineer or the undergraduate in an honors program. Strictly speaking, the individual volumes are not textbooks, although they are intended to teach, the guiding principle being that if something is worth explaining, it is worth explaining fully. This has necessarily restricted the scope of the series, but the selection of topics should give the reader a sound basis for further study.
Theory Of Matrix Algorithms
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Author : Peter Brucker
language : en
Publisher:
Release Date : 1974
Theory Of Matrix Algorithms written by Peter Brucker and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Mathematics categories.
Software For Roundoff Analysis Of Matrix Algorithms
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Author : Webb Miller
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Software For Roundoff Analysis Of Matrix Algorithms written by Webb Miller and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Computer Science and Applied Mathematics: A Series of Monographs and Textbooks: Software for Roundoff Analysis of Matrix Algorithms focuses on the presentation of techniques and software tools for analyzing the propagation of rounding error in matrix algorithms. The publication looks into some elements of error analysis, concepts from linear algebra and analysis, and directed graphs. Discussions focus on arithmetic graphs, sums of path products, linear transformations, Minkowski sums and Cartesian products, and elementary concepts from analysis. The text then examines software for roundoff analysis, including rounding and perturbations of the computational problem, comparing rounding errors with problem sensitivity, reverse condition numbers, and comparing two algorithms. The book ponders on case studies, as well as Gaussian elimination with iterative improvement, Cholesky factorization, Gauss-Jordan elimination, variants of the Gram-Schmidt method, and Cholesky factors after rank-one modifications. The text is a valuable reference for researchers interested in the techniques and software tools involved in the analysis of the propagation of rounding error in matrix algorithms.
Hierarchical Matrices Algorithms And Analysis
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Author : Wolfgang Hackbusch
language : en
Publisher: Springer
Release Date : 2015-12-21
Hierarchical Matrices Algorithms And Analysis written by Wolfgang Hackbusch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-21 with Mathematics categories.
This self-contained monograph presents matrix algorithms and their analysis. The new technique enables not only the solution of linear systems but also the approximation of matrix functions, e.g., the matrix exponential. Other applications include the solution of matrix equations, e.g., the Lyapunov or Riccati equation. The required mathematical background can be found in the appendix. The numerical treatment of fully populated large-scale matrices is usually rather costly. However, the technique of hierarchical matrices makes it possible to store matrices and to perform matrix operations approximately with almost linear cost and a controllable degree of approximation error. For important classes of matrices, the computational cost increases only logarithmically with the approximation error. The operations provided include the matrix inversion and LU decomposition. Since large-scale linear algebra problems are standard in scientific computing, the subject of hierarchical matrices is of interest to scientists in computational mathematics, physics, chemistry and engineering.
Matrix Computations On Systolic Type Arrays
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Author : Jaime Moreno
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Matrix Computations On Systolic Type Arrays written by Jaime Moreno 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 2012-12-06 with Technology & Engineering categories.
Matrix Computations on Systolic-Type Arrays provides a framework which permits a good understanding of the features and limitations of processor arrays for matrix algorithms. It describes the tradeoffs among the characteristics of these systems, such as internal storage and communication bandwidth, and the impact on overall performance and cost. A system which allows for the analysis of methods for the design/mapping of matrix algorithms is also presented. This method identifies stages in the design/mapping process and the capabilities required at each stage. Matrix Computations on Systolic-Type Arrays provides a much needed description of the area of processor arrays for matrix algorithms and of the methods used to derive those arrays. The ideas developed here reduce the space of solutions in the design/mapping process by establishing clear criteria to select among possible options as well as by a-priori rejection of alternatives which are not adequate (but which are considered in other approaches). The end result is a method which is more specific than other techniques previously available (suitable for a class of matrix algorithms) but which is more systematic, better defined and more effective in reaching the desired objectives. Matrix Computations on Systolic-Type Arrays will interest researchers and professionals who are looking for systematic mechanisms to implement matrix algorithms either as algorithm-specific structures or using specialized architectures. It provides tools that simplify the design/mapping process without introducing degradation, and that permit tradeoffs between performance/cost measures selected by the designer.
Fast Reliable Algorithms For Matrices With Structure
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Author : T. Kailath
language : en
Publisher: SIAM
Release Date : 1999-01-01
Fast Reliable Algorithms For Matrices With Structure written by T. Kailath and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-01 with Computers categories.
This book deals with the combined issues of speed and numerical reliability in algorithm development.