Revised simplex method: Difference between revisions

Content deleted Content added
Basis representation: Added the other notable ftran operation, calculating the transformed incoming column. Assuming primal you need that for the ratio test.
Basis representation: it does not matter what the vectors are, so use generic symbols
Line 194:
:<math>
\begin{align}
\boldsymbol{B x_Bz} & = \boldsymbol{by}, \text\
\boldsymbol{ and B}^{\mathrm{T}} \boldsymbol{B t_kz} & = \boldsymbol{a_ky}, \\.
\boldsymbol{B}^{\mathrm{T}} \boldsymbol{\lambda} & = \boldsymbol{c_B}.
\end{align}
</math>
 
Instead of refactorizing {{math|'''''B'''''}}, usually an [[LU factorization]] is directly updated after each pivot operation, for which purpose there exist several strategies such as the Forrest-TomlinForrest−Tomlin and Bartels−Golub methodmethods. However, the amount of data representing the updates as well as numerical errors builds up over time and makes periodic refactorization necessary.{{sfn|Morgan|1997|loc=§2}}{{sfn|Nocedal|Wright|2006|p=372|loc=§13.4}}
 
==Notes and references==