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.
