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\par
\chapter{{\tt Iter}: Iterative Methods}
\par
{\tt Iter} is composed of 5 Krylov space iterative methods, PCG (Preconditioned Conjugate
Gradients), BiCGStab, TFQMR, and BGMRES (Block GMRES),
and MLBiCGStab.
(For references, see top comments in codes.)
The intent of these methods is to provide the user of {\bf SPOOLES} with an
easy way to evaluate the effectiveness of the approximate factorizations belonging
to the {\tt FrontMtx} object. To further facilitate the evaluation we have included
a single call {\tt driver} that can run anyone of the methods we have provided with the
type of preconditioner desired. For each iterative method we allow for left and right
preconditioning. Also, for each method, except BGMRES, we allow for real or
complex matrices.
\par
Because our intent was to provide a simple means to test the effectiveness of the
preconditioners, these implementations are not parallel (neither shared or distributed
memory). However, they were intentionally written to be consistent in style and form
so that they could be easily adapted to exploit the parallelism that is in {\bf SPOOLES}.
All iterative methods use the basic structure {\tt DenseMtx} for handling the intermediate
vectors and performing the matrix multiplications and system solves. By doing this
we have also anticipated the eventual movement to block iterative methods and the
{\tt DenseMtx} structure can remain the basic structure. There are a few basic
utilities that have been added, which are discribed in this section, upon which the
iterative methods were built. These are provided to aid the experienced {\bf SPOOLES}
user with an ability to develop additional iterative methods, as seen fit.
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