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Exploiting Hidden Structure In Matrix Computations Algorithms And Applications
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Book Synopsis Exploiting Hidden Structure in Matrix Computations: Algorithms and Applications by : Michele Benzi
Download or read book Exploiting Hidden Structure in Matrix Computations: Algorithms and Applications written by Michele Benzi and published by Springer. This book was released on 2017-01-24 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on special matrices and matrices which are in some sense `near’ to structured matrices, this volume covers a broad range of topics of current interest in numerical linear algebra. Exploitation of these less obvious structural properties can be of great importance in the design of efficient numerical methods, for example algorithms for matrices with low-rank block structure, matrices with decay, and structured tensor computations. Applications range from quantum chemistry to queuing theory. Structured matrices arise frequently in applications. Examples include banded and sparse matrices, Toeplitz-type matrices, and matrices with semi-separable or quasi-separable structure, as well as Hamiltonian and symplectic matrices. The associated literature is enormous, and many efficient algorithms have been developed for solving problems involving such matrices. The text arose from a C.I.M.E. course held in Cetraro (Italy) in June 2015 which aimed to present this fast growing field to young researchers, exploiting the expertise of five leading lecturers with different theoretical and application perspectives.
Book Synopsis Smart Algorithms for Multimedia and Imaging by : Michael N. Rychagov
Download or read book Smart Algorithms for Multimedia and Imaging written by Michael N. Rychagov and published by Springer Nature. This book was released on 2021-05-05 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents prospective, industrially proven methods and software solutions for storing, processing, and viewing multimedia content on digital cameras, camcorders, TV, and mobile devices. Most of the algorithms described here are implemented as systems on chip firmware or as software products and have low computational complexity and memory consumption. In the four parts of the book, which contains a total of 16 chapters, the authors address solutions for the conversion of images and videos by super-resolution, depth estimation and control and mono-to-stereo (2D to 3D) conversion; display applications by video editing; the real-time detection of sport episodes; and the generation and reproduction of natural effects. The practical principles of machine learning are illustrated using technologies such as image classification as a service, mobile user profiling, and automatic view planning with dictionary-based compressed sensing in magnetic resonance imaging. The implementation of these technologies in mobile devices is discussed in relation to algorithms using a depth camera based on a colour-coded aperture, the animated graphical abstract of an image, a motion photo, and approaches and methods for iris recognition on mobile platforms. The book reflects the authors’ practical experience in the development of algorithms for industrial R&D and the commercialization of technologies. Explains digital techniques for digital cameras, camcorders, TV, mobile devices; Offers essential algorithms for the processing pipeline in multimedia devices and accompanying software tools; Features advanced topics on data processing, addressing current technology challenges.
Book Synopsis Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 by : Jens M. Melenk
Download or read book Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 written by Jens M. Melenk and published by Springer Nature. This book was released on 2023-06-30 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume features high-quality papers based on the presentations at the ICOSAHOM 2020+1 on spectral and high order methods. The carefully reviewed articles cover state of the art topics in high order discretizations of partial differential equations. The volume presents a wide range of topics including the design and analysis of high order methods, the development of fast solvers on modern computer architecture, and the application of these methods in fluid and structural mechanics computations.
Book Synopsis Parallel Algorithms for Matrix Computations by : K. Gallivan
Download or read book Parallel Algorithms for Matrix Computations written by K. Gallivan and published by SIAM. This book was released on 1990-01-01 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes a selection of important parallel algorithms for matrix computations. Reviews the current status and provides an overall perspective of parallel algorithms for solving problems arising in the major areas of numerical linear algebra, including (1) direct solution of dense, structured, or sparse linear systems, (2) dense or structured least squares computations, (3) dense or structured eigenvaluen and singular value computations, and (4) rapid elliptic solvers. The book emphasizes computational primitives whose efficient execution on parallel and vector computers is essential to obtain high performance algorithms. Consists of two comprehensive survey papers on important parallel algorithms for solving problems arising in the major areas of numerical linear algebra--direct solution of linear systems, least squares computations, eigenvalue and singular value computations, and rapid elliptic solvers, plus an extensive up-to-date bibliography (2,000 items) on related research.
Book Synopsis Matrix Computations by : Gene H. Golub
Download or read book Matrix Computations written by Gene H. Golub and published by JHU Press. This book was released on 1996-10-15 with total page 734 pages. Available in PDF, EPUB and Kindle. Book excerpt: Revised and updated, the third edition of Golub and Van Loan's classic text in computer science provides essential information about the mathematical background and algorithmic skills required for the production of numerical software. This new edition includes thoroughly revised chapters on matrix multiplication problems and parallel matrix computations, expanded treatment of CS decomposition, an updated overview of floating point arithmetic, a more accurate rendition of the modified Gram-Schmidt process, and new material devoted to GMRES, QMR, and other methods designed to handle the sparse unsymmetric linear system problem.
Book Synopsis Structured Matrices and Polynomials by : Victor Pan
Download or read book Structured Matrices and Polynomials written by Victor Pan and published by Springer Science & Business Media. This book was released on 2001-06-26 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Structured matrices serve as a natural bridge between the areas of algebraic computations with polynomials and numerical matrix computations, allowing cross-fertilization of both fields. This book covers most fundamental numerical and algebraic computations with Toeplitz, Hankel, Vandermonde, Cauchy, and other popular structured matrices. Throughout the computations, the matrices are represented by their compressed images, called displacements, enabling both a unified treatment of various matrix structures and dramatic saving of computer time and memory. The resulting superfast algorithms allow further dramatic parallel acceleration using FFT and fast sine and cosine transforms. Included are specific applications to other fields, in particular, superfast solutions to: various fundamental problems of computer algebra; the tangential Nevanlinna--Pick and matrix Nehari problems The primary intended readership for this work includes researchers, algorithm designers, and advanced graduate students in the fields of computations with structured matrices, computer algebra, and numerical rational interpolation. The book goes beyond research frontiers and, apart from very recent research articles, includes yet unpublished results. To serve a wider audience, the presentation unfolds systematically and is written in a user-friendly engaging style. Only some preliminary knowledge of the fundamentals of linear algebra is required. This makes the material accessible to graduate students and new researchers who wish to study the rapidly exploding area of computations with structured matrices and polynomials. Examples, tables, figures, exercises, extensive bibliography, and index lend this text to classroom use or self-study.
Book Synopsis Matrix Algorithms by : G. W. Stewart
Download or read book Matrix Algorithms written by G. W. Stewart and published by SIAM. This book was released on 1998-08-01 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Advances in Computational Intelligence Systems by : George Panoutsos
Download or read book Advances in Computational Intelligence Systems written by George Panoutsos and published by Springer Nature. This book was released on with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Matrix Computations and Semiseparable Matrices by : Raf Vandebril
Download or read book Matrix Computations and Semiseparable Matrices written by Raf Vandebril and published by JHU Press. This book was released on 2007-12-18 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years several new classes of matrices have been discovered and their structure exploited to design fast and accurate algorithms. In this new reference work, Raf Vandebril, Marc Van Barel, and Nicola Mastronardi present the first comprehensive overview of the mathematical and numerical properties of the family's newest member: semiseparable matrices. The text is divided into three parts. The first provides some historical background and introduces concepts and definitions concerning structured rank matrices. The second offers some traditional methods for solving systems of equations involving the basic subclasses of these matrices. The third section discusses structured rank matrices in a broader context, presents algorithms for solving higher-order structured rank matrices, and examines hybrid variants such as block quasiseparable matrices. An accessible case study clearly demonstrates the general topic of each new concept discussed. Many of the routines featured are implemented in Matlab and can be downloaded from the Web for further exploration.
Book Synopsis Sparse Matrix Computations by : James R. Bunch
Download or read book Sparse Matrix Computations written by James R. Bunch and published by Academic Press. This book was released on 2014-05-10 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sparse Matrix Computations is a collection of papers presented at the 1975 Symposium by the same title, held at Argonne National Laboratory. This book is composed of six parts encompassing 27 chapters that contain contributions in several areas of matrix computations and some of the most potential research in numerical linear algebra. The papers are organized into general categories that deal, respectively, with sparse elimination, sparse eigenvalue calculations, optimization, mathematical software for sparse matrix computations, partial differential equations, and applications involving sparse matrix technology. This text presents research on applied numerical analysis but with considerable influence from computer science. In particular, most of the papers deal with the design, analysis, implementation, and application of computer algorithms. Such an emphasis includes the establishment of space and time complexity bounds and to understand the algorithms and the computing environment. This book will prove useful to mathematicians and computer scientists.
Author :G. W. Stewart Publisher :Society for Industrial and Applied Mathematics ISBN 13 :9780898714142 Total Pages :184 pages Book Rating :4.7/5 (141 download)
Book Synopsis Matrix Algorithms: Volume 1, Basic Decompositions by : G. W. Stewart
Download or read book Matrix Algorithms: Volume 1, Basic Decompositions written by G. W. Stewart and published by Society for Industrial and Applied Mathematics. This book was released on 1998-08-01 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thorough, concise, and superbly written volume is the first in a self-contained five-volume series devoted to matrix algorithms. It focuses on the computation of matrix decompositions - 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 computation and applications of the LU and QR decompositions. The series is aimed at the nonspecialist who needs more than black-box proficiency with matrix computations. A certain knowledge of elementary analysis and linear algebra is assumed, as well as a reasonable amount of programming experience. The guiding principle, that if something is worth explaining, it is worth explaining fully, has necessarily restricted the scope of the series, but the selection of topics should give the reader a sound basis for further study.
Book Synopsis Parallel Algorithms for Matrix Computations by :
Download or read book Parallel Algorithms for Matrix Computations written by and published by . This book was released on 1990 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Handbook for Matrix Computations by : Thomas F. Coleman
Download or read book Handbook for Matrix Computations written by Thomas F. Coleman and published by SIAM. This book was released on 1988-01-01 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Download or read book Matrix Methods written by Vadim Olshevsky and published by World Scientific. This book was released on 2010 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix methods provide the key to many problems in pure and applied mathematics. However, linear algebra theory, numerical algorithms and matrices in FEM/BEM applications usually live as if in three separate worlds. In this volume, maybe for the first time ever, they are compiled together as one entity as it was at the Moscow meeting, where the algebraic part was impersonated by Hans Schneider, algorithms by Gene Golub, and applications by Guri Marchuk. All topics intervened in plenary sessions are specially categorized into three sections of this volume. --
Book Synopsis Structured Matrices in Numerical Linear Algebra by : Dario Bini
Download or read book Structured Matrices in Numerical Linear Algebra written by Dario Bini and published by . This book was released on 2019 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers selected contributions presented at the INdAM Meeting Structured Matrices in Numerical Linear Algebra: Analysis, Algorithms and Applications, held in Cortona, Italy on September 4-8, 2017. Highlights cutting-edge research on Structured Matrix Analysis, it covers theoretical issues, computational aspects, and applications alike. The contributions, written by authors from the foremost international groups in the community, trace the main research lines and treat the main problems of current interest in this field. The book offers a valuable resource for all scholars who are interested in this topic, including researchers, PhD students and post-docs.
Book Synopsis Parallelism in Matrix Computations by : Efstratios Gallopoulos
Download or read book Parallelism in Matrix Computations written by Efstratios Gallopoulos and published by Springer. This book was released on 2015-07-25 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Computational Matrix Analysis by : Alan J. Laub
Download or read book Computational Matrix Analysis written by Alan J. Laub and published by SIAM. This book was released on 2012-01-01 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using an approach that author Alan Laub calls "matrix analysis for grown-ups," this new textbook introduces fundamental concepts of numerical linear algebra and their application to solving certain numerical problems arising in state-space control and systems theory. It is written for advanced undergraduate and beginning graduate students and can be used as a follow-up to Matrix Analysis for Scientists and Engineers (SIAM, 2005), a compact single-semester introduction to matrix analysis for engineers and computational scientists by the same author. Computational Matrix Analysis provides readers with a one-semester introduction to numerical linear algebra; an introduction to statistical condition estimation in book form for the first time; and an overview of certain computational problems in control and systems theory. The book features a number of elements designed to help students learn to use numerical linear algebra in day-to-day computing or research, including a brief review of matrix analysis, including notation, and an introduction to finite (IEEE) arithmetic; discussion and examples of conditioning, stability, and rounding analysis; an introduction to mathematical software topics related to numerical linear algebra; a thorough introduction to Gaussian elimination, along with condition estimation techniques; coverage of linear least squares, with orthogonal reduction and QR factorization; variants of the QR algorithm; and applications of the discussed algorithms.
