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The Resource Parallelism in Matrix Computations, by Efstratios Gallopoulos, Bernard Philippe, Ahmed H. Sameh, (electronic resource)
Parallelism in Matrix Computations, by Efstratios Gallopoulos, Bernard Philippe, Ahmed H. Sameh, (electronic resource)
Resource Information
The item Parallelism in Matrix Computations, by Efstratios Gallopoulos, Bernard Philippe, Ahmed H. Sameh, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Parallelism in Matrix Computations, by Efstratios Gallopoulos, Bernard Philippe, Ahmed H. Sameh, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 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 singularvalue 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. Â 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 stateoftheart systems, as well as several algorithms that are presented for the first time, focusing on the opportunities for parallelism and algorithm robustness
 Language
 eng
 Edition
 1st ed. 2016.
 Extent
 XXX, 473 p. 58 illus.
 Contents

 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
 Isbn
 9789401771887
 Label
 Parallelism in Matrix Computations
 Title
 Parallelism in Matrix Computations
 Statement of responsibility
 by Efstratios Gallopoulos, Bernard Philippe, Ahmed H. Sameh
 Subject

 Computeraided engineering
 Engineering
 Numerical and Computational Physics
 Physics
 Applied mathematics
 Appl.Mathematics/Computational Methods of Engineering
 Computer science  Mathematics
 Mathematics of Computing
 Electronic resources
 Computeraided engineering
 Engineering mathematics
 Engineering
 Engineering
 Computer science  Mathematics
 Physics
 Physics
 Applied mathematics
 Engineering mathematics
 Computational Science and Engineering
 Engineering mathematics
 Computer science  Mathematics
 Computeraided engineering
 ComputerAided Engineering (CAD, CAE) and Design
 Applied mathematics
 Language
 eng
 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 singularvalue 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. Â 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 stateoftheart systems, as well as several algorithms that are presented for the first time, focusing on the opportunities for parallelism and algorithm robustness
 http://library.link/vocab/creatorName
 Gallopoulos, E. J.
 Image bit depth
 0
 LC call number

 TA329348
 TA640643
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorDate
 1950
 http://library.link/vocab/relatedWorkOrContributorName

 Philippe, Bernard
 Sameh, Ahmed
 SpringerLink
 Series statement
 Scientific Computation,
 http://library.link/vocab/subjectName

 Engineering
 Computer science
 Computeraided engineering
 Computer science
 Physics
 Applied mathematics
 Engineering mathematics
 Engineering
 Appl.Mathematics/Computational Methods of Engineering
 Computational Science and Engineering
 Numerical and Computational Physics
 Mathematics of Computing
 ComputerAided Engineering (CAD, CAE) and Design
 Label
 Parallelism in Matrix Computations, by Efstratios Gallopoulos, Bernard Philippe, Ahmed H. Sameh, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 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
 Dimensions
 unknown
 Edition
 1st ed. 2016.
 Extent
 XXX, 473 p. 58 illus.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9789401771887
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9789401771887
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9789401771887
 Label
 Parallelism in Matrix Computations, by Efstratios Gallopoulos, Bernard Philippe, Ahmed H. Sameh, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 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
 Dimensions
 unknown
 Edition
 1st ed. 2016.
 Extent
 XXX, 473 p. 58 illus.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9789401771887
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9789401771887
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9789401771887
Subject
 Appl.Mathematics/Computational Methods of Engineering
 Applied mathematics
 Applied mathematics
 Applied mathematics
 Computational Science and Engineering
 Computer science  Mathematics
 Computer science  Mathematics
 Computer science  Mathematics
 ComputerAided Engineering (CAD, CAE) and Design
 Computeraided engineering
 Computeraided engineering
 Computeraided engineering
 Electronic resources
 Engineering
 Engineering
 Engineering
 Engineering mathematics
 Engineering mathematics
 Engineering mathematics
 Mathematics of Computing
 Numerical and Computational Physics
 Physics
 Physics
 Physics
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