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Adding local short description: "Concept in mathematics", overriding Wikidata description "iterative method for the numerical solution of nonsymmetric linear systems" |
m The second equation in the derivation was inconsistent with the second recurrence relation right above the section, i.e. a P was used in the recurrence relation in place of a T. It's easy to check that the latter is correct, so I fixed that mistake. |
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which entails the necessity of a recurrence relation for {{math|<var>Q<sub>i</sub></var>('''<var>A</var>''')<var>T<sub>i</sub></var>('''<var>A</var>''')'''<var>r</var>'''<sub>0</sub>}}. This can also be derived from the BiCG relations:
:{{math|<var>Q<sub>i</sub></var>('''<var>A</var>''')<var>T<sub>i</sub></var>('''<var>A</var>''')'''<var>r</var>'''<sub>0</sub> {{=}} <var>Q<sub>i</sub></var>('''<var>A</var>''')<var>P<sub>i</sub></var>('''<var>A</var>''')'''<var>r</var>'''<sub>0</sub> + <var>β</var><sub><var>i</var>+1</sub>('''<var>I</var>''' − <var>ω<sub>i</sub>'''A'''</var>)<var>Q</var><sub><var>i</var>−1</sub>('''<var>A</var>''')<var>
Similarly to defining {{math|<var>'''r̃'''<sub>i</sub></var>}}, BiCGSTAB defines
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