The problem of solving large, sparse, linear systems of algebraic
equations is vital in scientific computing, even for applications
originating from quite different fields. A Survey of Preconditioned
Iterative Methods presents an up to date overview of iterative
methods for numerical solution of such systems. Typically, the
methods considered are well suited for the kind of systems arising
from the discretization of partial differential equations. The
focus of this presentation is on the family of Krylov subspace
solvers, of which the Conjugate Gradient algorithm is a typical
example. In addition to an introduction to the basic principles of
such methods, a large number of specific algorithms for symmetric
and nonsymmetric problems are discussed. When solving linear
systems by iteration, a preconditioner is usually introduced in
order to speed up convergence. In many cases, the selection of a
proper preconditioner is crucial to the resulting computational
performance. For this reason, this book pays special attention to
different preconditioning strategies. Although aimed at a wide
audience, the presentation assumes that the reader has basic
knowledge of linear algebra, and to some extent, of partial
differential equations. The comprehensive bibliography in this
survey is provides an entry point to the enormous amount of
published research in the field of iterative methods.
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