The two main approaches for solving non-Hermitian linear systems of equations
with Krylov subspace methods differ in the schemes used to generate suitable basis
vectors for computing corrections to the approximate solution.
In the early 90s, the introduction of look-ahead techniques to
stabilize the Lanczos process along with the QMR method made
biorthogonalization methods an attractive approach due to their (for all
practical purposes) linear cost in storage and arithmetic.
Moreover, these methods, even if used without look-ahead techniques,
often outperform those based on orthogonalisation such as GMRES, which constitute
the second main approach.
This is because methods of the latter class must be
restarted or truncated in order to make their application feasible.
Recently a number of acceleration techniques have been proposed which
attempt to compensate for the effects of restarting and truncation, thus
closing the gap between orthogonalisation and
In this work we complement our recent analysis  of three
of the more popular of these acceleration schemes with a careful
numerical study which attempts to identify the strengths and
weaknesses of each scheme.
 M. Eiermann, O.G. Ernst and O. Schneider. Analysis of acceleration strategies for restarted minimal residual methods. J. Comp. Appl. Math 123 (2000) pp. 262--292.