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Amanda2277 (talk | contribs) →Unpreconditioned BiCGSTAB: Added reference to paper showing numerical impact of choosing a different rhat0 |
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## {{math|<var>β</var> {{=}} (<var>ρ<sub>i</sub></var>/<var>ρ</var><sub><var>i</var>−1</sub>)(<var>α</var>/<var>ω</var>)}}
## {{math|<var>'''p'''<sub>i</sub></var> {{=}} '''<var>r</var>'''<sub><var>i</var></sub> + <var>β</var>('''<var>p</var>'''<sub><var>i</var>−1</sub> − <var>ω</var>'''<var>v</var>''')}}
In some cases, choosing the vector {{math|'''<var>r̂</var>'''<sub>0</sub>}} randomly improves numerical stability<ref>{{Cite journal |last=Schoutrop |first=Chris |last2=Boonkkamp |first2=Jan ten Thije |last3=Dijk |first3=Jan van |date=2022-06 |title=Reliability Investigation of BiCGStab and IDR Solvers for the Advection-Diffusion-Reaction Equation |url=https://doi.org/10.4208/cicp.OA-2021-0182 |journal=Communications in Computational Physics |language=en |volume=32 |issue=1 |pages=156–188 |doi=10.4208/cicp.oa-2021-0182 |issn=1815-2406}}</ref>.
===Preconditioned BiCGSTAB===
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