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Applied Numerical Linear Algebra (Paperback, New)
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Applied Numerical Linear Algebra (Paperback, New)
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Designed for use by first-year graduate students from a variety of
engineering and scientific disciplines, this comprehensive textbook
covers the solution of linear systems, least squares problems,
eigenvalue problems, and the singular value decomposition. The
author, who helped design the widely-used LAPACK and ScaLAPACK
linear algebra libraries, draws on this experience to present
state-of-the-art techniques for these problems, including
recommendations of which algorithms to use in a variety of
practical situations. This is the book for you if you are looking
for a textbook that:* Teaches state-of-the-art techniques for
solving linear algebra problems. * Covers the most important
methods for dense and sparse problems.* Presents both the
mathematical background and good software techniques. * Is
self-contained, assuming only a good undergraduate background in
linear algebra. Algorithms are derived in a mathematically
illuminating way, including condition numbers and error bounds.
Direct and iterative algorithms, suitable for dense and sparse
matrices, are discussed. Algorithm design for modern computer
architectures, where moving data is often more expensive than
arithmetic operations, is discussed in detail, using LAPACK as an
illustration. There are many numerical examples throughout the text
and in the problems at the ends of chapters, most of which are
written in Matlab and are freely available on the Web. Material
either not available elsewhere, or presented quite differently in
other textbooks, includes:* A discussion of the impact of modern
cache-based computer memories on algorithm design.* Frequent
recommendations and pointers in the text to the best software
currently available, including a detailed performance comparison of
state-of-the-art software for eigenvalue and least squares
problems, and a description of sparse direct solvers for serial and
parallel machines. * A discussion of iterative methods ranging from
Jacobi's method to multigrid and domain decomposition, with
performance comparisons on a model problem.* A great deal of
Matlab-based software, available on the Web, which either
implements algorithms presented in the book, produces the figures
in the book, or is used in homework problems.* Numerical examples
drawn from fields ranging from mechanical vibrations to
computational geometry.* High-accuracy algorithms for solving
linear systems and eigenvalue problems, along with tighter
"relative" error bounds. * Dynamical systems interpretations of
some eigenvalue algorithms. Demmel discusses several current
research topics, making students aware of both the lively research
taking place and connections to other parts of numerical analysis,
mathematics, and computer science. Some of this material is
developed in questions at the end of each chapter, which are marked
Easy, Medium, or Hard according to their difficulty. Some questions
are straightforward, supplying proofs of lemmas used in the text.
Others are more difficult theoretical or computing problems.
Questions involving significant amounts of programming are marked
Programming. The computing questions mainly involve Matlab
programming, and others involve retrieving, using, and perhaps
modifying LAPACK code from NETLIB.
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