{{seealso|Simplex method#Degeneracy: Stalling and cycling}}
Because the revised simplex method is mathematically equivalent to the simplex method, it also suffers from degeneracy, where a pivot operation does not results in a decrease in {{math|'''''c'''''<mathsup>\boldsymbol{c}^{\mathrm{T}} \boldsymbol{x}</mathsup>'''''x'''''}}, and a chain of pivot operations causes the basis to cycle. A perturbation or lexicographic strategy can be used to prevent cycling and guarantee termination.{{sfn|Nocedal|Wright|2006|p=381|loc=§13.5}}
===Basis representation===
Two [[System of linear equations|linear systems]] involving <math>\boldsymbol{{math|'''''B'''''}}</math> are present in the revised simplex method:
:<math>
Line 199:
</math>
Instead of refactorizing <math>\boldsymbol{{math|'''''B'''''}}</math>, usually an [[LU factorization]] is directly updated after each pivot operation, for which purpose there exist several strategies such as the Bartels−Golub method. 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}}
