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050		4	_aQA76.58 _b.G35 2016 EB
082	0	4	_a519
100	1		_aGallopoulos, Efstratios _9100611 _0Local
245	1	0	_aParallelism in matrix computations _cby Efstratios Gallopoulos, Bernard Philippe, Ahmed H. Sameh
250			_a1st ed
260			_aDordrecht _bSpringer _c2016
300			_a1 recurso en línea (XXX, 473 p.) _b58 ilustraciones
336			_aTexto (visual) _btxt _2rdacontent
337			_aelectrónico _bc _2rdamedia
338			_arecurso electrónico _bcr _2rdacarrier
490	1		_aScientific Computation _x1434-8322
505	0		_aList 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
520			_aThis 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
710	2		_aSpringerLink (Online service) _0Local _9106996
942			_2lcc _cLE
988			_aEBOOK, EBSPRINGER
650		7	_aProceso paralelo (Informática) _0comprobar BNE20012044022 _2embne _9158747
650	0	4	_9666321 _aIngeniería asistida por ordenador _0LocalX
650		7	_aMatrices (Matemáticas) _0comprobar BNE19901022555 _2embne _9142711
700	1		_aPhilippe, Bernard _9100612 _0Local
700	1		_aSameh, Ahmed H. _9100613 _0Local
830		0	_aScientific Computation _x1434-8322 _9134318 _0Local
856	4	0	_uhttps://go.openathens.net/redirector/universidadeuropea.es?url=https://link.springer.com/book/10.1007/978-94-017-7188-7 _zAcceso a este recurso digital (usuarios Universidad Europea de Madrid)
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