# On Implementing a Two-Step Interior Point Method for Solving Linear Programs
## 4 Conclusions
\begin{table}
\begin{tabular}{c c c c} \hline
**Name** & **Regap** & \(\|\mathbf{Ax-b}\|\) & \(\|\mathbf{c-s-A^{T}y}\|\) \\ \hline agg2 & \(3.23\times 10^{-8}\) & \(9.15\times 10^{-12}\) & \(3.34\times 10^{-6}\) \\ agg2 & \(7.21\times 10^{-7}\) & \(5.27\times 10^{-13}\) & \(3.34\times 10^{-6}\) \\ agg2 & \(2.03\times 10^{-9}\) & \(3.29\times 10^{-14}\) & \(3.37\times 10^{-6}\) \\ \hline agg3 & \(5.27\times 10^{-7}\) & \(1.13\times 10^{-10}\) & \(2.82\times 10^{-6}\) \\ agg3 & \(5.77\times 10^{-7}\) & \(4.40\times 10^{-11}\) & \(2.82\times 10^{-6}\) \\ agg3 & \(2.62\times 10^{-7}\) & \(1.01\times 10^{-11}\) & \(3.24\times 10^{-6}\) \\ \hline bandm & \(8.64\times 10^{-7}\) & \(7.02\times 10^{-13}\) & \(1.76\times 10^{-3}\) \\ bandm & \(1.50\times 10^{-7}\) & \(4.43\times 10^{-15}\) & \(1.76\times 10^{-7}\) \\ bandm & \(7.66\times 10^{-7}\) & \(2.86\times 10^{-13}\) & \(8.31\times 10^{-9}\) \\ \hline beaconfd & \(6.09\times 10^{-9}\) & \(7.13\times 10^{-5}\) & \(3.75\times 10^{-8}\) \\ beaconfd & \(4.26\times 10^{-8}\) & \(1.25\times 10^{-8}\) & \(3.75\times 10^{-8}\) \\ beaconfd & \(2.405\times 10^{-8}\) & \(6.97\times 10^{-9}\) & \(1.52\times 10^{-8}\) \\ \hline blend & \(5.83\times 10^{-7}\) & \(2.87\times 10^{-16}\) & \(2.78\times 10^{-6}\) \\ blend & \(5.25\times 10^{-7}\) & \(6.43\times 10^{-10}\) & \(2.78\times 10^{-6}\) \\ blend & \(9.32\times 10^{-7}\) & \(7.54\times 10^{-14}\) & \(7.10\times 10^{-5}\) \\ \hline bnl2 & \(9.79\times 10^{-7}\) & \(1.65\times 10^{-16}\) & \(3.37\times 10^{-3}\) \\ bnl2 & \(8.55\times 10^{-7}\) & \(2.27\times 10^{-16}\) & \(3.37\times 10^{-3}\) \\ bnl2 & \(6.19\times 10^{-7}\) & \(1.97\times 10^{-16}\) & \(2.66\times 10^{-2}\) \\ \hline capri & \(2.34\times 10^{-9}\) & \(2.57\times 10^{-16}\) & \(2.41\times 10^{-7}\) \\ capri & \(1.57\times 10^{-7}\) & \(1.45\times 10^{-10}\) & \(2.41\times 10^{-7}\) \\ capri & \(4.77\times 10^{-7}\) & \(6.37\times 10^{-10}\) & \(7.62\times 10^{-6}\) \\ \hline chemcom & \(3.88\times 10^{-9}\) & \(1.48\times 10^{-16}\) & \(6.08\times 10^{-9}\) \\ chemcom & \(1.52\times 10^{-7}\) & \(1.66\times 10^{-12}\) & \(6.08\times 10^{-9}\) \\ chemcom & \(1.98\times 10^{-7}\) & \(1.72\times 10^{-12}\) & \(6.11\times 10^{-8}\) \\ \hline czprob & \(9.42\times 10^{-7}\) & \(1.01\times 10^{-12}\) & \(1.59\times 10^{-3}\) \\ czprob & \(8.18\times 10^{-7}\) & \(8.94\times 10^{-13}\) & \(1.59\times 10^{-3}\) \\ czprob & \(7.07\times 10^{-9}\) & \(2.98\times 10^{-13}\) & \(3.81\times 10^{-5}\) \\ \hline e226 & \(2.03\times 10^{-7}\) & \(3.85\times 10^{-15}\) & \(5.40\times 10^{-4}\) \\ e226 & \(2.95\times 10^{-7}\) & \(2.60\times 10^{-14}\) & \(5.40\times 10^{-4}\) \\ e226 & \(7.65\times 10^{-7}\) & \(3.31\times 10^{-16}\) & \(4.22\times 10^{-3}\) \\ \hlineffff800 & \(9.51\times 10^{-7}\) & \(1.16\times 10^{-10}\) & \(3.45\times 10^{-7}\) \\ffff800 & \(3.96\times 10^{-7}\) & \(8.72\times 10^{-11}\) & \(3.45\times 10^{-7}\) \\ffff800 & \(1.31\times 10^{-8}\) & \(1.65\times 10^{-10}\) & \(6.25\times 10^{-7}\) \\ \hline fit1p & \(8.80\times 10^{-7}\) & \(1.48\times 10^{-16}\) & \(1.02\times 10^{-5}\) \\ fit1p & \(1.25\times 10^{-7}\) & \(1.39\times 10^{-11}\) & \(1.02\times 10^{-5}\) \\ fit1p & \(1.01\times 10^{-7}\) & \(1.26\times 10^{-11}\) & \(7.49\times 10^{-10}\) \\ \hline forest6 & \(6.54\times 10^{-8}\) & \(6.95\times 10^{-16}\) & \(1.71\times 10^{-6}\) \\ forest6 & \(8.14\times 10^{-7}\) & \(5.54\times 10^{-12}\) & \(1.71\times 10^{-6}\) \\ forest6 & \(8.59\times 10^{-7}\) & \(5.57\times 10^{-12}\) & \(3.51\times 10^{-5}\) \\ \hline ganges & \(7.87\times 10^{-7}\) & \(1.48\times 10^{-16}\) & \(2.40\times 10^{-7}\) \\ ganges & \(5.00\times 10^{-7}\) & \(6.77\times 10^{-12}\) & \(2.40\times 10^{-7}\) \\ ganges & \(4.25\times 10^{-7}\) & \(4.97\times 10^{-12}\) & \(3.41\times 10^{-8}\) \\ \hline gfrd\_pnc & \(1.88\times 10^{-8}\) & \(9.77\times 10^{-17}\) & \(1.24\times 10^{-6}\) \\ gfrd\_pnc & \(2.99\times 10^{-7}\) & \(1.69\times 10^{-16}\) & \(1.24\times 10^{-6}\) \\ gfrd\_pnc & \(2.11\times 10^{-7}\) & \(1.57\times 10^{-16}\) & \(3.98\times 10^{-6}\) \\ \hline israel & \(8.63\times 10^{-7}\) & \(3.42\times 10^{-16}\) & \(4.00\times 10^{-6}\) \\ israel & \(2.37\times 10^{-7}\) & \(7.63\times 10^{-14}\) & \(4.00\times 10^{-6}\) \\ israel & \(2.33\times 10^{-7}\) & \(7.32\times 10^{-14}\) & \(3.99\times 10^{-6}\) \\ \hline \end{tabular}
\end{table}