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Parallelism in Matrix Computations (Paperback, Softcover reprint of the original 1st ed. 2016)
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Parallelism in Matrix Computations (Paperback, Softcover reprint of the original 1st ed. 2016)
Series: Scientific Computation
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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 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.
General
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