Exploiting Hidden Structure In Matrix Computations Algorithms And Applications

Author : Michele Benzi,Dario Bini,Daniel Kressner,Hans Munthe-Kaas,Charles Van Loan
Publisher : Springer
Page : 406 pages
File Size : 45,7 Mb
Release : 2017-01-24
Category : Mathematics
ISBN : 9783319498874

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Exploiting Hidden Structure in Matrix Computations: Algorithms and Applications by Michele Benzi,Dario Bini,Daniel Kressner,Hans Munthe-Kaas,Charles Van Loan Pdf

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.

Author : Michael N. Rychagov,Ekaterina V. Tolstaya,Mikhail Y. Sirotenko
Publisher : Springer Nature
Page : 433 pages
File Size : 49,7 Mb
Release : 2021-05-05
Category : Technology & Engineering
ISBN : 9783030667412

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Smart Algorithms for Multimedia and Imaging by Michael N. Rychagov,Ekaterina V. Tolstaya,Mikhail Y. Sirotenko Pdf

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.

Author : Jens M. Melenk,Ilaria Perugia,Joachim Schöberl,Christoph Schwab
Publisher : Springer Nature
Page : 571 pages
File Size : 47,7 Mb
Release : 2023-06-30
Category : Mathematics
ISBN : 9783031204326

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Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 by Jens M. Melenk,Ilaria Perugia,Joachim Schöberl,Christoph Schwab Pdf

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.

Author : K. Gallivan,M. Heath,E. Ng,B. Peyton,R. Plemmons,J. Ortega,C. Romine,A. Sameh,R. Voigt
Publisher : SIAM
Page : 207 pages
File Size : 51,9 Mb
Release : 1990-01-01
Category : Mathematics
ISBN : 1611971705

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Parallel Algorithms for Matrix Computations by K. Gallivan,M. Heath,E. Ng,B. Peyton,R. Plemmons,J. Ortega,C. Romine,A. Sameh,R. Voigt Pdf

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.

Author : Victor Pan
Publisher : Springer Science & Business Media
Page : 312 pages
File Size : 51,8 Mb
Release : 2001-06-26
Category : Computers
ISBN : 0817642404

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Structured Matrices and Polynomials by Victor Pan Pdf

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.

Author : Gene H. Golub,Charles F. Van Loan
Publisher : JHU Press
Page : 734 pages
File Size : 48,8 Mb
Release : 1996-10-15
Category : Mathematics
ISBN : 0801854148

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Matrix Computations by Gene H. Golub,Charles F. Van Loan Pdf

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.

Author : Åke Björck
Publisher : Springer
Page : 800 pages
File Size : 43,8 Mb
Release : 2014-10-07
Category : Mathematics
ISBN : 9783319050898

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Numerical Methods in Matrix Computations by Åke Björck Pdf

Matrix algorithms are at the core of scientific computing and are indispensable tools in most applications in engineering. This book offers a comprehensive and up-to-date treatment of modern methods in matrix computation. It uses a unified approach to direct and iterative methods for linear systems, least squares and eigenvalue problems. A thorough analysis of the stability, accuracy, and complexity of the treated methods is given. Numerical Methods in Matrix Computations is suitable for use in courses on scientific computing and applied technical areas at advanced undergraduate and graduate level. A large bibliography is provided, which includes both historical and review papers as well as recent research papers. This makes the book useful also as a reference and guide to further study and research work.

Author : G. W. Stewart
Publisher : SIAM
Page : 476 pages
File Size : 41,5 Mb
Release : 1998-08-01
Category : Mathematics
ISBN : 9780898714142

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Matrix Algorithms by G. W. Stewart Pdf

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.

Author : Raf Vandebril,Marc Van Barel,Nicola Mastronardi
Publisher : JHU Press
Page : 594 pages
File Size : 52,5 Mb
Release : 2008-01-14
Category : Mathematics
ISBN : 9780801896798

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Matrix Computations and Semiseparable Matrices by Raf Vandebril,Marc Van Barel,Nicola Mastronardi Pdf

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.

Author : George Panoutsos
Publisher : Springer Nature
Page : 594 pages
File Size : 53,6 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9783031555688

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Advances in Computational Intelligence Systems by George Panoutsos Pdf

Author : James R. Bunch,Donald J. Rose
Publisher : Academic Press
Page : 468 pages
File Size : 51,6 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483263403

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Sparse Matrix Computations by James R. Bunch,Donald J. Rose Pdf

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 : Thomas F. Coleman,Charles Van Loan
Publisher : SIAM
Page : 271 pages
File Size : 50,9 Mb
Release : 1988-01-01
Category : Mathematics
ISBN : 1611971047

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Handbook for Matrix Computations by Thomas F. Coleman,Charles Van Loan Pdf

Provides the user with a step-by-step introduction to Fortran 77, BLAS, LINPACK, and MATLAB. It is a reference that spans several levels of practical matrix computations with a strong emphasis on examples and "hands on" experience.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 40,9 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9789814469555

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Matrix Methods: Theory, Algorithms and Applications by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 197 pages
File Size : 43,6 Mb
Release : 1990
Category : Algorithms
ISBN : OCLC:1150944255

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Parallel Algorithms for Matrix Computations by Anonim Pdf

Author : G. W. Stewart
Publisher : Society for Industrial and Applied Mathematics
Page : 184 pages
File Size : 54,6 Mb
Release : 1998-08-01
Category : Mathematics
ISBN : 0898714141

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Matrix Algorithms: Volume 1, Basic Decompositions by G. W. Stewart Pdf

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.