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Parallelism in matrix computations [electronic resource] / Efstratios Gallopoulos, Bernard Philippe, Ahmed H. Sameh.

Gallopoulos, Efstratios, author.; Philippe, B., author.; Sameh, Ahmed, author.
2015
QA76.58
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Title
Parallelism in matrix computations [electronic resource] / Efstratios Gallopoulos, Bernard Philippe, Ahmed H. Sameh.
Author
Gallopoulos, Efstratios, author.
ISBN
9789401771887 (electronic book)
940177188X (electronic book)
9789401771870
DOI
https://doi.org/10.1007/978-94-017-7188-7
Published
Dordrecht : Springer, [2015]
Copyright
©2016
Language
English
Description
1 online resource (xxx, 473 pages) : illustrations.
Item Number
10.1007/978-94-017-7188-7 doi
Call Number
QA76.58
Dewey Decimal Classification
004/.35
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Digital File Characteristics
text file PDF
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed July 27, 2015).
Added Author
Philippe, B., author.
Sameh, Ahmed, author.
Series
Scientific computation.
Available in Other Form
Print version: 9789401771870
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Online Access
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List of Figures
List of Tables
List of Algorithms
Notations used in the book
Part I Basics
Parallel Programming Paradigms
Computational Models
Principles of parallel programming
Fundamental kernels
Vector operations
Higher level BLAS
General organization for dense matrix factorizations
Sparse matrix computations
Part II Dense and special matrix computations
Recurrences and triangular systems
Definitions and examples
Linear recurrences
Implementations for a given number of processors
Nonlinear recurrences
General linear systems
Gaussian elimination
Pair wise pivoting
Block LU factorization
Remarks
Banded linear systems
LUbased schemes with partial pivoting
The Spike family of algorithms
The Spike balance scheme
A tearing based banded solver
Tridiagonal systems
Special linear systems
Vandermonde solvers
Banded Toeplitz linear systems solvers
Symmetric and Anti symmetric Decomposition (SAS)
Rapid elliptic solvers
Orthogonal factorization and linear least squares problems
Definitions
QR factorization via Givens rotations
QR factorization via Householder reductions
Gram Schmidt orthogonalization
Normal equations vs. orthogonal reductions
Hybrid algorithms when m>>n
Orthogonal factorization of block angular matrices
Rank deficient linear least squares problems
The symmetric eigenvalue and singular value problems
The Jacobi algorithms
Tridiagonalization based schemes
Bidiagonalization via Householder reduction
Part III Sparse matrix computations
Iterative schemes for large linear systems
An example
Classical splitting methods
Polynomial methods
Preconditioners
A tearing based solver for generalized banded preconditioners
Row projection methods for large non symmetric linear systems
Multiplicative Schwarz preconditioner with GMRES
Large symmetric eigenvalue problems
Computing dominant eigenpairs and spectral transformations
The Lanczos method
A block Lanczos approach for solving symmetric perturbed standard eigenvalue problems
The Davidson methods
The trace minimization method for the symmetric generalized eigenvalue problem
The sparse singular value problem
Part IV Matrix functions and characteristics
Matrix functions and the determinant
Matrix functions
Determinants
Computing the matrix pseudospectrum
Grid based methods
Dimensionality reduction on the domain: Methods based on path following
Dimensionality reduction on the matrix: Methods based on projection
Notes
References.

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