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 cancelation effects occur. This may lead to a less accurate solution than suggested by the updated residual (see Van der Vorst [207]). The method tends to diverge if the starting guess is close to the solution.

Mon Nov 20 08:52:54 EST 1995