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Often one observes a speed of convergence for CGS that is about twice
as fast as for BiCG, which is in agreement with the observation that
the same ``contraction'' operator is applied twice. However, there is
no reason that the ``contraction'' operator, even if it really reduces
the initial residual , should also reduce the once reduced
vector
. This is evidenced by the often
highly irregular convergence behavior of CGS
. One should be aware of
the fact that local corrections to the current solution may be so
large that cancellation effects occur. This may lead to a less
accurate solution than suggested by the updated residual
(see Van der Vorst [202]).
The method tends to diverge if the starting guess is close to the solution.