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Convergence

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.