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The convergence behavior of QMR is typically much smoother than for BiCG. Freund and Nachtigal [100] present quite general error bounds which show that QMR may be expected to converge about as fast as GMRES. From a relation between the residuals in BiCG and QMR (Freund and Nachtigal ([100], relation (5.10)) one may deduce that at phases in the iteration process where BiCG makes significant progress, QMR has arrived at about the same approximation for . On the other hand, when BiCG makes no progress at all, QMR may still show slow convergence.

The look-ahead steps in the QMR method prevent breakdown in all cases but the so-called ``incurable breakdown''.