# On Implementing a Two-Step Interior Point Method for Solving Linear Programs
## 4 Conclusions
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Name** & **Regap** & \(\|\mathbf{Ax-b}\|\) & \(\|\mathbf{c-s-A^{T}y}\|\) \\ \hline lotti & \(1.07\times 10^{-8}\) & \(2.34\times 10^{-14}\) & \(1.89\times 10^{-8}\) \\ lotti & \(4.72\times 10^{-7}\) & \(4.05\times 10^{-12}\) & \(1.89\times 10^{-8}\) \\ lotti & \(2.23\times 10^{-7}\) & \(1.84\times 10^{-12}\) & \(5.32\times 10^{-7}\) \\ \hline maro\_r7 & \(2.36\times 10^{-10}\) & \(2.94\times 10^{-16}\) & \(7.53\times 10^{-9}\) \\ maro\_r7 & \(6.67\times 10^{-8}\) & \(2.92\times 10^{-12}\) & \(7.53\times 10^{-9}\) \\ maro\_r7 & \(5.15\times 10^{-8}\) & \(2.059\times 10^{-12}\) & \(1.82\times 10^{-9}\) \\ \hline pilot87 & \(2.10\times 10^{-5}\) & \(7.50\times 10^{-12}\) & \(3.58\times 10^{-7}\) \\ pilot87 & \(3.86\times 10^{-5}\) & \(2.46\times 10^{-12}\) & \(3.58\times 10^{-7}\) \\ pilot87 & \(1.35\times 10^{-5}\) & \(2.76\times 10^{-12}\) & \(2.85\times 10^{-7}\) \\ \hline pilot & \(2.26\times 10^{-7}\) & \(7.30\times 10^{-13}\) & \(5.62\times 10^{-7}\) \\ pilot & \(1.62\times 10^{-6}\) & \(1.00\times 10^{-13}\) & \(5.62\times 10^{-7}\) \\ pilot & \(1.53\times 10^{-6}\) & \(7.56\times 10^{-14}\) & \(1.55\times 10^{-6}\) \\ \hline pilot\_we & \(9.70\times 10^{-7}\) & \(6.77\times 10^{-15}\) & \(9.06\times 10^{-4}\) \\ pilot\_we & \(2.87\times 10^{-7}\) & \(4.01\times 10^{-15}\) & \(9.06\times 10^{-4}\) \\ pilot\_we & \(8.19\times 10^{-7}\) & \(6.18\times 10^{-15}\) & \(1.27\times 10^{-3}\) \\ \hline sc50a & \(9.73\times 10^{-7}\) & \(7.74\times 10^{-17}\) & \(7.90\times 10^{-3}\) \\ sc50a & \(6.08\times 10^{-7}\) & \(1.39\times 10^{-12}\) & \(7.901\times 10^{-3}\) \\ sc50a & \(7.08\times 10^{-7}\) & \(7.57\times 10^{-16}\) & \(3.92\times 10^{-2}\) \\ \hline sc50b & \(9.94\times 10^{-7}\) & \(1.36\times 10^{-16}\) & \(5.45\times 10^{-3}\) \\ sc50b & \(6.46\times 10^{-7}\) & \(3.58\times 10^{-14}\) & \(5.45\times 10^{-3}\) \\ sc50b & \(4.58\times 10^{-7}\) & \(1.90\times 10^{-16}\) & \(2.71\times 10^{-3}\) \\ \hline sc105 & \(1.02\times 10^{-7}\) & \(1.02\times 10^{-16}\) & \(1.20\times 10^{-2}\) \\ sc105 & \(4.64\times 10^{-7}\) & \(8.09\times 10^{-13}\) & \(1.20\times 10^{-2}\) \\ sc105 & \(6.63\times 10^{-7}\) & \(2.12\times 10^{-16}\) & \(9.76\times 10^{-3}\) \\ \hline sc205 & \(5.80\times 10^{-9}\) & \(1.12\times 10^{-16}\) & \(3.80\times 10^{-6}\) \\ sc205 & \(3.35\times 10^{-7}\) & \(9.02\times 10^{-13}\) & \(3.80\times 10^{-6}\) \\ sc205 & \(5.83\times 10^{-7}\) & \(1.69\times 10^{-16}\) & \(9.60\times 10^{-3}\) \\ \hline sc2 gr25 & \(6.25\times 10^{-7}\) & \(1.32\times 10^{-16}\) & \(2.79\times 10^{-6}\) \\ scagr25 & \(2.11\times 10^{-7}\) & \(5.24\times 10^{-12}\) & \(2.79\times 10^{-6}\) \\ scagr25 & \(2.80\times 10^{-7}\) & \(8.46\times 10^{-11}\) & \(6.52\times 10^{-5}\) \\ \hline scfkm1 & \(9.01\times 10^{-7}\) & \(1.82\times 10^{-10}\) & \(4.43\times 10^{-6}\) \\ scfkm1 & \(1.74\times 10^{-7}\) & \(9.71\times 10^{-10}\) & \(4.43\times 10^{-6}\) \\ scfkm1 & \(9.94\times 10^{-7}\) & \(1.45\times 10^{-9}\) & \(7.66\times 10^{-6}\) \\ \hline scfkm2 & \(7.87\times 10^{-7}\) & \(5.19\times 10^{-10}\) & \(1.62\times 10^{-6}\) \\ scfkm2 & \(4.25\times 10^{-7}\) & \(1.41\times 10^{-10}\) & \(1.62\times 10^{-6}\) \\ scfkm2 & \(9.46\times 10^{-7}\) & \(1.25\times 10^{-10}\) & \(3.06\times 10^{-6}\) \\ \hline scfkm3 & \(9.61\times 10^{-7}\) & \(8.06\times 10^{-9}\) & \(7.08\times 10^{-7}\) \\ scfkm3 & \(1.57\times 10^{-7}\) & \(3.51\times 10^{-10}\) & \(7.08\times 10^{-7}\) \\ scfkm3 & \(1.60\times 10^{-7}\) & \(3.86\times 10^{-10}\) & \(6.77\times 10^{-7}\) \\ \hline scrs8 & \(8.13\times 10^{-7}\) & \(5.25\times 10^{-13}\) & \(4.79\times 10^{-8}\) \\ scrs8 & \(7.91\times 10^{-7}\) & \(1.84\times 10^{-13}\) & \(4.79\times 10^{-8}\) \\ scrs8 & \(2.03\times 10^{-7}\) & \(1.82\times 10^{-14}\) & \(2.15\times 10^{-8}\) \\ \hline scagr7 & \(9.96\times 10^{-7}\) & \(1.33\times 10^{-16}\) & \(1.01\times 10^{-6}\) \\ scagr7 & \(7.30\times 10^{-7}\) & \(1.71\times 10^{-16}\) & \(1.01\times 10^{-6}\) \\ scagr7 & \(3.32\times 10^{-7}\) & \(4.26\times 10^{-14}\) & \(6.08\times 10^{-6}\) \\ \hline scsd1 & \(6.18\times 10^{-7}\) & \(1.18\times 10^{-16}\) & \(1.18\times 10^{-7}\) \\ scsd1 & \(6.90\times 10^{-7}\) & \(1.04\times 10^{-16}\) & \(1.18\times 10^{-7}\) \\ scsd1 & \(7.51\times 10^{-7}\) & \(8.19\times 10^{-17}\) & \(1.08\times 10^{-5}\) \\ \hline \hline \end{tabular}
\end{table}