It has a curved steel wall that is connected to a pivot element or ball-joint by steel trusses.
The choice of the pivot element at each iteration is one of the most critical step in simplex type algorithms.
Also note that for quick sort, it is relatively difficult to exercise and measure the path yielding the worst case behavior since it depends on the pivot element selection.
Extension of the basis according to the columns in which no pivot element could be found during the Gaussian elimination in step 1).
Recall further that all entries to the right of, above and below a pivot element equal to 1 must be zero.
The column permutation matrix P is constructed during the GJE process while applying the leading row and column selection rules (pivot element selection).
Note that in numerical GJE algorithms the typical leading row and column selection rule consists of choosing a pivot element with largest absolute value for maximal numerical stability.
In SympyCore [ 11] the leading row and column selection rule consists of choosing such a pivot element that minimizes the number of row operations for minimal computation time.
In addition, SympyCore [ 11] minimizes the number of operations by its pivot element selection rule (see Methods) to reduce computational time and this has added benefit of reducing the chance of coefficient explosion.
One of the advantage of using GJE is that it allows one to influence the pivot element selection rules so that a preferred flux basis for the system will be obtained.
