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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Interative Methods for Solving Linear Systems (Paperback, Illustrated Ed)
Loot Price: R2,511
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Interative Methods for Solving Linear Systems (Paperback, Illustrated Ed)
Series: Frontiers in Applied Mathematics, v. 17
Expected to ship within 12 - 17 working days
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Much recent research has concentrated on the efficient solution of
large sparse or structured linear systems using iterative methods.
A language loaded with acronyms for a thousand different algorithms
has developed, and it is often difficult even for specialists to
identify the basic principles involved. Here is a book that focuses
on the analysis of iterative methods. The author includes the most
useful algorithms from a practical point of view and discusses the
mathematical principles behind their derivation and analysis.
Several questions are emphasized throughout: Does the method
converge? If so, how fast? Is it optimal, among a certain class? If
not, can it be shown to be near-optimal? The answers are presented
clearly, when they are known, and remaining important open
questions are laid out for further study. Greenbaum includes
important material on the effect of rounding errors on iterative
methods that has not appeared in other books on this subject.
Additional important topics include a discussion of the open
problem of finding a provably near-optimal short recurrence for
non-Hermitian linear systems; the relation of matrix properties
such as the field of values and the pseudospectrum to the
convergence rate of iterative methods; comparison theorems for
preconditioners and discussion of optimal preconditioners of
specified forms; introductory material on the analysis of
incomplete Cholesky, multigrid, and domain decomposition
preconditioners, using the diffusion equation and the neutron
transport equation as example problems. A small set of recommended
algorithms and implementations is included.
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