04870nam 2200625 450 991082307200332120200520144314.01-118-76172-31-118-76171-5(CKB)3710000000538848(EBL)4205695(MiAaPQ)EBC4205695(Au-PeEL)EBL4205695(CaPaEBR)ebr11136006(CaONFJC)MIL881795(OCoLC)933442910(PPN)198592817(EXLCZ)99371000000053884820160113h20162016 uy 0engur|n|---|||||rdacontentrdamediardacarrierParallel scientific computing /Frédéric Magoulès, François-Xavier Roux, Guillaume HouzeauxLondon, England ;Hoboken, New Jersey :ISTE :Wiley,2016.©20161 online resource (287 p.)Description based upon print version of record.1-118-76168-5 1-84821-581-9 Includes bibliographical references and index.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 algebra4.2. 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 factorization8.2. 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 Matrices11.1. 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 matrices13.2. 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 methods15.3. Schur complement methodParallel processing (Electronic computers)Industrial applicationsParallel algorithmsIndustrial applicationsIndustrial engineeringMathematicsParallel processing (Electronic computers)Industrial applications.Parallel algorithmsIndustrial applications.Industrial engineeringMathematics.004/.35Magoulès F(Frédéric),633188Roux François-XavierHouzeaux G(Guillaume),MiAaPQMiAaPQMiAaPQBOOK9910823072003321Parallel scientific computing3997008UNINA