Parallelism in matrix computations. ([2015])

• Record Type: Book
• Further Information: Note: Efstratios Gallopoulos, Bernard Philippe, Ahmed H. Sameh.
• Authors: Gallopoulos, E. J (Efstratios J.); Philippe, Bernard, 1950-; Sameh, Ahmed
• 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.
• Publisher Details: Dordrecht : Springer
• Publication Date: 2015
• Copyright Date: 2016
• Extent: 1 online resource (xxx, 473 pages), illustrations
• Subjects: 004/.35; Parallel processing (Electronic computers); Matrices; Computer algorithms; Computer algorithms; Matrices; Parallel processing (Electronic computers); Electronic books
• Languages: English
• ISBNs: 9789401771887; 9401771871; 9789401771870
• Related ISBNs: 940177188X; 9789401771870
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (SpringerLink, viewed July 27, 2015).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.