Parallel scientific computing / / Frédéric Magoulès, François-Xavier Roux, Guillaume Houzeaux

• Record Nr.: UNINA9910823072003321
• Autore: Magoulès F (Frédéric)
• Pubbl/distr/stampa: London, England ; ; Hoboken, New Jersey : , : ISTE : , : Wiley, , 2016; ©2016
• ISBN: 1-118-76172-3; 1-118-76171-5
• Descrizione fisica: 1 online resource (287 p.)
• Disciplina: 004/.35
• Soggetti: Parallel processing (Electronic computers) - Industrial applications; Parallel algorithms - Industrial applications; Industrial engineering - Mathematics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Table of Contents; Title; Copyright; Preface; Introduction; 1 Computer Architectures; 1.1. Different types of parallelism; 1.2. Memory architecture; 1.3. Hybrid architecture; 2 Parallelization and Programming Models; 2.1. Parallelization; 2.2. Performance criteria; 2.3. Data parallelism; 2.4. Vectorization: a case study; 2.5. Message-passing; 2.6. Performance analysis; 3 Parallel Algorithm Concepts; 3.1. Parallel algorithms for recurrences; 3.2. Data locality and distribution: product of matrices; 4 Basics of Numerical Matrix Analysis; 4.1. Review of basic notions of linear algebra; 4.2. Properties of matrices5 Sparse Matrices; 5.1. Origins of sparse matrices; 5.2. Parallel formation of sparse matrices: shared memory; 5.3. Parallel formation by block of sparse matrices: distributed memory; 6 Solving Linear Systems; 6.1. Direct methods; 6.2. Iterative methods; 7 LU Methods for Solving Linear Systems; 7.1. Principle of LU decomposition; 7.2. Gauss factorization; 7.3. Gauss-Jordan factorization; 7.4. Crout and Cholesky factorizations for symmetric matrices; 8 Parallelization of LU Methods for Dense Matrices; 8.1. Block factorization; 8.2. Implementation of block factorization in a message-passing ; environment8.3. Parallelization of forward and backward substitutions; 9 LU Methods for Sparse Matrices; 9.1. Structure of factorized matrices; 9.2. Symbolic factorization and renumbering; 9.3. Elimination trees; 9.4. Elimination trees and dependencies; 9.5. Nested dissections; 9.6. Forward and backward substitutions; 10 Basics of Krylov Subspaces; 10.1. Krylov subspaces; 10.2. Construction of the Arnoldi basis; 11 Methods with Complete Orthogonalization for Symmetric Positive Definite Matrices; 11.1. Construction of the Lanczos basis for symmetric matrices11.2. The Lanczos method; 11.3. The conjugate gradient method; 11.4. Comparison with the gradient method; 11.5. Principle of preconditioning for symmetric positive definite matrices; 12 Exact Orthogonalization Methods for Arbitrary Matrices; 12.1. The GMRES method; 12.2. The case of symmetric matrices: the MINRES method; 12.3. The ORTHODIR method; 12.4. Principle of preconditioning for non-symmetric matrices; 13 Biorthogonalization Methods for Non-symmetric Matrices; 13.1. Lanczos biorthogonal basis for non-symmetric matrices; 13.2. The non-symmetric Lanczos method13.3. The biconjugate gradient method: BiCG; 13.4. The quasi-minimal residual method: QMR; 13.5. The BiCGSTAB; 14 Parallelization of Krylov Methods; 14.1. Parallelization of dense matrix-vector product; 14.2. Parallelization of sparse matrix-vector product based on node sets; 14.3. Parallelization of sparse matrix-vector product based on element sets; 14.4. Parallelization of the scalar product; 14.5. Summary of the parallelization of Krylov methods; 15 Parallel Preconditioning Methods; 15.1. Diagonal; 15.2. Incomplete factorization methods; 15.3. Schur complement method