results are summarized in Table \[table1\]. All initial points are selected as $[0, \ldots, 0]^{\Tr}$. For the first variant of Klee-Minty cube [@greenberg97], using the most two negative elements of $\bar{c}_{N^k}$ to choose the entering variables (described in Remark \[mostNeg\]) is better than the strategy of Dantzig’s rule which uses the most negative element of $\bar{c}_{N^k}$ to choose the entering variable. The pivot rule with the most two negative elements uses half of the iterations of Dantzig’s rule but the iteration numbers still increase exponentially fast. When the size $m \ge 18$, the program freezes because iteration numbers are very big and the computational time is very long.

Algorithm \[mainAlg\] is much more impressive. For all problems in three variants, only one iteration is needed to find the optimal solution, except for the problem with dimension $m=200$ in variant 2 [@ibrahima13] because Matlab R2016a on computer Dell Inspiron 3847 cannot store the big value (bigger than 10E+310) in vector $\b$. This shows that the estimated bound of Theorem \[mainThe\] is reachable.

We also compared the tests result with the one in [@ibrahima13] which uses randomized pivot method. For $m=100$, the randomized pivot method uses more than $1000$ iterations to find 