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Previous: Quasi-Minimal Residual (QMR)
Up: Quasi-Minimal Residual (QMR)
Next: Implementation
Previous Page: Quasi-Minimal Residual (QMR)
Next Page: Implementation
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''.