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==Generalization==
BiCGSTAB can be viewed as a combination of BiCG and [[GMRES]] where each BiCG step is followed by a GMRES({{math|1}}) (i.e., GMRES restarted at each step) step to repair the irregular convergence behavior of CGS, as an improvement of which BiCGSTAB was developed. However, due to the use of degree-one minimum residual polynomials, such repair may not be effective if the matrix {{math|'''<var>A</var>'''}} has large complex eigenpairs. In such cases, BiCGSTAB is likely to stagnate, as confirmed by numerical experiments.
One may expect that higher-degree minimum residual polynomials may better handle this situation. This gives rise to algorithms including BiCGSTAB2{{ref|bicgstab2}} and the more general BiCGSTAB({{math|<var>l</var>}}){{ref|bicgstab(l)}}. In BiCGSTAB({{math|<var>l</var>}}), a GMRES({{math|<var>l</var>}}) step follows every {{math|<var>l</var>}} BiCG steps. BiCGSTAB2 is equivalent to BiCGSTAB({{math|<var>l</var>}}) with {{math|<var>l</var> {{=}} 2}}.
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