Matrix Algorithms
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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.
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
Eigenvalue Algorithms For Symmetric Hierarchical Matrices
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Author : Thomas Mach
language : en
Publisher: Thomas Mach
Release Date : 2012
Eigenvalue Algorithms For Symmetric Hierarchical Matrices written by Thomas Mach and has been published by Thomas Mach this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
This thesis is on the numerical computation of eigenvalues of symmetric hierarchical matrices. The numerical algorithms used for this computation are derivations of the LR Cholesky algorithm, the preconditioned inverse iteration, and a bisection method based on LDL factorizations. The investigation of QR decompositions for H-matrices leads to a new QR decomposition. It has some properties that are superior to the existing ones, which is shown by experiments using the HQR decompositions to build a QR (eigenvalue) algorithm for H-matrices does not progress to a more efficient algorithm than the LR Cholesky algorithm. The implementation of the LR Cholesky algorithm for hierarchical matrices together with deflation and shift strategies yields an algorithm that require O(n) iterations to find all eigenvalues. Unfortunately, the local ranks of the iterates show a strong growth in the first steps. These H-fill-ins makes the computation expensive, so that O(n³) flops and O(n²) storage are required. Theorem 4.3.1 explains this behavior and shows that the LR Cholesky algorithm is efficient for the simple structured Hl-matrices. There is an exact LDLT factorization for Hl-matrices and an approximate LDLT factorization for H-matrices in linear-polylogarithmic complexity. This factorizations can be used to compute the inertia of an H-matrix. With the knowledge of the inertia for arbitrary shifts, one can compute an eigenvalue by bisectioning. The slicing the spectrum algorithm can compute all eigenvalues of an Hl-matrix in linear-polylogarithmic complexity. A single eigenvalue can be computed in O(k²n log^4 n). Since the LDLT factorization for general H-matrices is only approximative, the accuracy of the LDLT slicing algorithm is limited. The local ranks of the LDLT factorization for indefinite matrices are generally unknown, so that there is no statement on the complexity of the algorithm besides the numerical results in Table 5.7. The preconditioned inverse iteration computes the smallest eigenvalue and the corresponding eigenvector. This method is efficient, since the number of iterations is independent of the matrix dimension. If other eigenvalues than the smallest are searched, then preconditioned inverse iteration can not be simply applied to the shifted matrix, since positive definiteness is necessary. The squared and shifted matrix (M-mu I)² is positive definite. Inner eigenvalues can be computed by the combination of folded spectrum method and PINVIT. Numerical experiments show that the approximate inversion of (M-mu I)² is more expensive than the approximate inversion of M, so that the computation of the inner eigenvalues is more expensive. We compare the different eigenvalue algorithms. The preconditioned inverse iteration for hierarchical matrices is better than the LDLT slicing algorithm for the computation of the smallest eigenvalues, especially if the inverse is already available. The computation of inner eigenvalues with the folded spectrum method and preconditioned inverse iteration is more expensive. The LDLT slicing algorithm is competitive to H-PINVIT for the computation of inner eigenvalues. In the case of large, sparse matrices, specially tailored algorithms for sparse matrices, like the MATLAB function eigs, are more efficient. If one wants to compute all eigenvalues, then the LDLT slicing algorithm seems to be better than the LR Cholesky algorithm. If the matrix is small enough to be handled in dense arithmetic (and is not an Hl(1)-matrix), then dense eigensolvers, like the LAPACK function dsyev, are superior. The H-PINVIT and the LDLT slicing algorithm require only an almost linear amount of storage. They can handle larger matrices than eigenvalue algorithms for dense matrices. For Hl-matrices of local rank 1, the LDLT slicing algorithm and the LR Cholesky algorithm need almost the same time for the computation of all eigenvalues. For large matrices, both algorithms are faster than the dense LAPACK function dsyev.
Matrix Computations And Semiseparable Matrices
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Author : Raf Vandebril
language : en
Publisher: JHU Press
Release Date : 2008-12-15
Matrix Computations And Semiseparable Matrices written by Raf Vandebril and has been published by JHU Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-15 with Mathematics categories.
The general properties and mathematical structures of semiseparable matrices were presented in volume 1 of Matrix Computations and Semiseparable Matrices. In volume 2, Raf Vandebril, Marc Van Barel, and Nicola Mastronardi discuss the theory of structured eigenvalue and singular value computations for semiseparable matrices. These matrices have hidden properties that allow the development of efficient methods and algorithms to accurately compute the matrix eigenvalues. This thorough analysis of semiseparable matrices explains their theoretical underpinnings and contains a wealth of information on implementing them in practice. Many of the routines featured are coded in Matlab and can be downloaded from the Web for further exploration.
Algorithms And Architectures For Parallel Processing
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Author : Yang Xiang
language : en
Publisher: Springer
Release Date : 2012-09-04
Algorithms And Architectures For Parallel Processing written by Yang Xiang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-04 with Computers categories.
The two volume set LNCS 7439 and 7440 comprises the proceedings of the 12th International Conference on Algorithms and Architectures for Parallel Processing, ICA3PP 2012, as well as some workshop papers of the CDCN 2012 workshop which was held in conjunction with this conference. The 40 regular paper and 26 short papers included in these proceedings were carefully reviewed and selected from 156 submissions. The CDCN workshop attracted a total of 19 original submissions, 8 of which are included in part II of these proceedings. The papers cover many dimensions of parallel algorithms and architectures, encompassing fundamental theoretical approaches, practical experimental results, and commercial components and systems.
Introduction To Parallel Algorithms And Architectures
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Author : F. Thomson Leighton
language : en
Publisher: Elsevier
Release Date : 2014-05-12
Introduction To Parallel Algorithms And Architectures written by F. Thomson Leighton and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Mathematics categories.
Introduction to Parallel Algorithms and Architectures: Arrays Trees Hypercubes provides an introduction to the expanding field of parallel algorithms and architectures. This book focuses on parallel computation involving the most popular network architectures, namely, arrays, trees, hypercubes, and some closely related networks. Organized into three chapters, this book begins with an overview of the simplest architectures of arrays and trees. This text then presents the structures and relationships between the dominant network architectures, as well as the most efficient parallel algorithms for a wide variety of problems. Other chapters focus on fundamental results and techniques and on rigorous analysis of algorithmic performance. This book discusses as well a hybrid of network architecture based on arrays and trees called the mesh of trees. The final chapter deals with the most important properties of hypercubes. This book is a valuable resource for readers with a general technical background.
Knot Insertion And Deletion Algorithms For B Spline Curves And Surfaces
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Author : Ronald N. Goldman
language : en
Publisher: SIAM
Release Date : 1993-01-01
Knot Insertion And Deletion Algorithms For B Spline Curves And Surfaces written by Ronald N. Goldman and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-01-01 with Mathematics categories.
New approaches to knot insertion and deletion are presented in this unique, detailed approach to understanding, analyzing, and rendering B-spline curves and surfaces. Computer scientists, mechanical engineers, and programmers and analysts involved in CAD and CAGD will find innovative, practical applications using the blossoming approach to knot insertion, factored knot insertion, and knot deletion, as well as comparisons of many knot insertion algorithms. This book also serves as an excellent reference guide for graduate students involved in computer aided geometric design.
Advances In Computing And Information Icci 90
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Author : Selim G. Akl
language : en
Publisher: Springer Science & Business Media
Release Date : 1990
Advances In Computing And Information Icci 90 written by Selim G. Akl 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 1990 with Coding theory categories.
This volume contains selected and invited papers presented at the International Conference on Computing and Information, ICCI '90, Niagara Falls, Ontario, Canada, May 23-26, 1990. ICCI conferences provide an international forum for presenting new results in research, development and applications in computing and information. Their primary goal is to promote an interchange of ideas and cooperation between practitioners and theorists in the interdisciplinary fields of computing, communication and information theory. The four main topic areas of ICCI '90 are: - Information and coding theory, statistics and probability, - Foundations of computer science, theory of algorithms and programming, - Concurrency, parallelism, communications, networking, computer architecture and VLSI, - Data and software engineering, databases, expert systems, information systems, decision making, and AI methodologies.
Algorithms And Theory Of Computation Handbook
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Author : Mikhail J. Atallah
language : en
Publisher: CRC Press
Release Date : 1998-11-23
Algorithms And Theory Of Computation Handbook written by Mikhail J. Atallah and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-11-23 with Computers categories.
Algorithms and Theory of Computation Handbook is a comprehensive collection of algorithms and data structures that also covers many theoretical issues. It offers a balanced perspective that reflects the needs of practitioners, including emphasis on applications within discussions on theoretical issues. Chapters include information on finite precision issues as well as discussion of specific algorithms where algorithmic techniques are of special importance, including graph drawing, robotics, forming a VLSI chip, vision and image processing, data compression, and cryptography. The book also presents some advanced topics in combinatorial optimization and parallel/distributed computing. • applications areas where algorithms and data structuring techniques are of special importance • graph drawing • robot algorithms • VLSI layout • vision and image processing algorithms • scheduling • electronic cash • data compression • dynamic graph algorithms • on-line algorithms • multidimensional data structures • cryptography • advanced topics in combinatorial optimization and parallel/distributed computing
Embedded Artificial Intelligence
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Author : Bin Li
language : en
Publisher: Springer Nature
Release Date : 2024-09-06
Embedded Artificial Intelligence written by Bin Li and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-06 with Computers categories.
This book focuses on the emerging topic of embedded artificial intelligence and provides a systematic summary of its principles, platforms, and practices. In the section on principles, it analyzes three main approaches for implementing embedded artificial intelligence: cloud computing mode, local mode, and local-cloud collaborative mode. The book identifies five essential components for implementing embedded artificial intelligence: embedded AI accelerator chips, lightweight neural network algorithms, model compression techniques, compiler optimization techniques, and multi-level cascaded application frameworks. The platform section introduces mainstream embedded AI accelerator chips and software frameworks currently used in the industry. The practical part outlines the development process of embedded artificial intelligence and showcases real-world application examples with accompanying code. As a comprehensive guide to the emerging field of embedded artificial intelligence, the book offers rich and in-depth content, a clear and logical structure, and a balanced approach to both theoretical analysis and practical applications. It provides significant reference value and can serve as an introductory and reference guide for researchers, scholars, students, engineers, and professionals interested in studying and implementing embedded artificial intelligence.