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# Compiler Support for Sparse Matrix Computations: PhD Thesis by Aart J.C. Bik, Leiden University, 1996 (English Edition) livro de referência

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## Compiler Support for Sparse Matrix Computations: PhD Thesis by Aart J.C. Bik, Leiden University, 1996 (English Edition) livro de referência

- Autor: Aart J.C. Bik
- Data de publicação: 2018-05-26
- Tag: compiler, support, sparse, matrix, computations, thesis, leiden, university, english, edition

This PhD Thesis by Aart J.C. Bik (Leiden University, 1996) gives an in-depth presentation of the sparse compiler MT1, i.e., a special kind of source-to-source restructuring compiler that can automatically transform a dense program (in which all operations on matrices are implemented using two-dimensional arrays) into a semantically equivalent sparse program (operating on more complicated sparse data structures), thereby reducing storage requirements and computational time of the original application.

## Matrix Computations (Johns Hopkins Studies in the Mathematical Sciences) livro de referência

- Autor: Gene H Golub
- Editora: Johns Hopkins University Press
- Data de publicação: 2012-12-27
- ISBN: 1421408597
- Páginas: 781 pages
- Tag: matrix, computations, johns, hopkins, studies, mathematical, sciences

The fourth edition of Gene H. Golub and Charles F. Van Loan's classic is an essential reference for computational scientists and engineers in addition to researchers in the numerical linear algebra community. Anyone whose work requires the solution to a matrix problem and an appreciation of its mathematical properties will find this text useful and engaging.

This revision is a cover-to-cover expansion and renovation of the third edition. It now includes an introduction to tensor computations and brand new sections on • fast transforms• parallel LU• discrete Poisson solvers• pseudospectra• structured linear equation problems• structured eigenvalue problems• large-scale SVD methods• polynomial eigenvalue problems

*Matrix Computations* is packed with challenging problems, insightful derivations, and pointers to the literature—everything needed to become a matrix-savvy developer of numerical methods and software.

## Quaternion Matrix Computations livro de referência

- Autor: Musheng Wei
- Editora: Nova Science Pub Inc
- Data de publicação: 2018-10-11
- ISBN: 1536141216
- Tag: quaternion, matrix, computations

## Matrix Computations and Semiseparable Matrices: Linear Systems: Volume 2 livro de referência

- Autor: Raf Vandebril
- Editora: JHUP
- Data de publicação: 2010-06-01
- Páginas: 520 pages
- Tag: matrix, computations, semiseparable, matrices, linear, systems, volume

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.

## Matrix Computations and Semiseparable Matrices: Eigenvalue and Singular Value Methods: Volume 1 livro de referência

- Autor: Raf Vandebril
- Editora: JHUP
- Data de publicação: 2010-06-01
- Páginas: 584 pages
- Tag: matrix, computations, semiseparable, matrices, eigenvalue, singular, value, methods, volume

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.

## Exploiting Hidden Structure in Matrix Computations: Algorithms and Applications: Cetraro, Italy 2015 (Lecture Notes in Mathematics) livro de referência

- Autor: Michele Benzi
- Editora: Springer
- Data de publicação: 2017-03-06
- Páginas: 406 pages
- Tag: exploiting, hidden, structure, matrix, computations, algorithms, applications, cetraro, italy, lecture, notes, mathematics

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.

## Sparse Matrix Computations livro de referência

- Editora: Academic Press
- Data de publicação: 2014-05-10
- Páginas: 464 pages
- Tag: sparse, matrix, computations

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.

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.

## Parallelism in Matrix Computations (Scientific Computation) livro de referência

- Autor: Efstratios Gallopoulos
- Editora: Springer
- Data de publicação: 2015-07-25
- Páginas: 473 pages
- Tag: parallelism, matrix, computations, scientific, computation

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.

## Numerical Methods in Matrix Computations (Texts in Applied Mathematics) livro de referência

- Autor: Åke Björck
- Editora: Springer
- Data de publicação: 2014-10-07
- Páginas: 800 pages
- Tag: numerical, methods, matrix, computations, texts, applied, mathematics

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.

Åke Björck is a professor emeritus at the Department of Mathematics, Linköping University. He is a Fellow of the Society of Industrial and Applied Mathematics.

## Latent Variable Analysis and Signal Separation: 14th International Conference, LVA/ICA 2018, Guildford, UK, July 2-5, 2018, Proceedings livro de referência

- Editora: Springer
- Data de publicação: 2018-07-21
- ISBN: 3319937634
- Páginas: 600 pages
- Tag: latent, variable, analysis, signal, separation, international, conference, guildford, proceedings

This book constitutes the proceedings of the 14th International Conference on Latent Variable Analysis and Signal Separation, LVA/ICA 2018, held in Guildford, UK, in July 2018.

The 52 full papers were carefully reviewed and selected from 62 initial submissions.

As research topics the papers encompass a wide range of general mixtures of latent variables models but also theories and tools drawn from a great variety of disciplines such as structured tensor decompositions and applications; matrix and tensor factorizations; ICA methods; nonlinear mixtures; audio data and methods; signal separation evaluation campaign; deep learning and data-driven methods; advances in phase retrieval and applications; sparsity-related methods; and biomedical data and methods.