\begin{tabular}{|ccc|cc|cc|cc|} \hline
\multicolumn{3}{|c||}{Dim, Density, \& $\kappa(A)$} & \multicolumn{2}{|c|}{\% Reduction in $\kappa$} & \multicolumn{2}{|c|}{CPU Time (seconds)} &\multicolumn{2}{|c|}{Ratios Qu/Alg 3.1}\cr\cline{1-3}\cline{3-9}
  $n$ & density & $\kappa(A)$ & Qu et al. & Alg. 3.1 & Qu et al. & Alg 3.1 & $\kappa$ &  CPU \cr\hline
 1074 & 1.1e-02 & 2.6e+07 & 3.9e-10 & 8.6e+01 & 3.689 & 0.265 &  7.3 & 13.9 \cr\hline
 2003 & 2.1e-02 & 1.1e+10 & -3.6e-10 & 6.9e+01 & 10.561 & 0.140 &  3.2 & 75.2 \cr\hline
 3600 & 2.1e-03 & 1.8e+07 & 8.5e-07 & 5.8e+01 & 81.951 & 9.609 &  2.4 &  8.5 \cr\hline
 3134 & 4.6e-03 & 2.6e+12 & 2.6e-08 & 7.0e+01 & 23.667 & 0.421 &  3.3 & 56.2 \cr\hline
 3562 & 1.3e-02 & 1.9e+11 & 1.7e-09 & 7.8e+01 & 31.265 & 1.621 &  4.5 & 19.3 \cr\hline
 1922 & 8.2e-03 & 1.7e+08 & -1.1e-09 & 8.4e+01 & 9.038 & 0.096 &  6.2 & 93.9 \cr\hline
 4410 & 1.1e-02 & 9.5e+08 & 1.7e-07 & 8.3e+01 & 133.694 & 0.529 &  5.8 & 252.8 \cr\hline
  588 & 6.2e-02 & 2.8e+04 & 2.3e-04 & 9.2e+01 & 3.009 & 0.270 & 12.6 & 11.2 \cr\hline
  494 & 6.8e-03 & 2.4e+06 & 1.3e+01 & 3.3e+01 & 9.040 & 0.169 &  1.3 & 53.5 \cr\hline
  662 & 5.6e-03 & 7.9e+05 & 2.7e+01 & 4.5e+01 & 20.986 & 0.183 &  1.3 & 114.9 \cr\hline
  685 & 6.9e-03 & 4.2e+05 & 7.7e+01 & 4.1e+01 & 25.260 & 1.584 &  0.4 & 15.9 \cr\hline
 1824 & 1.2e-02 & 1.9e+06 & 6.3e-04 & 5.0e+01 & 24.960 & 0.303 &  2.0 & 82.5 \cr\hline
 2146 & 1.6e-02 & 1.7e+03 & 4.0e-04 & 4.7e+01 & 34.544 & 2.310 &  1.9 & 15.0 \cr\hline
 2910 & 2.1e-02 & 6.0e+06 & 2.0e-05 & 5.0e+01 & 98.717 & 0.434 &  2.0 & 227.3 \cr\hline
  237 & 1.8e-02 & 2.0e+07 & -3.6e-11 & 6.5e+01 & 0.323 & 0.036 &  2.8 &  8.9 \cr\hline
  957 & 4.5e-03 & 5.1e+09 & -5.3e-11 & 6.4e+01 & 2.352 & 0.114 &  2.8 & 20.7 \cr\hline
  100 & 5.9e-02 & 1.6e+03 & 1.9e+00 & 3.6e+01 & 0.678 & 0.486 &  1.5 &  1.4 \cr\hline
  468 & 2.4e-02 & 1.1e+04 & 3.6e+01 & 7.3e+01 & 6.012 & 1.116 &  2.3 &  5.4 \cr\hline
  729 & 8.7e-03 & 2.4e+09 & 2.6e-01 & 2.5e+01 & 3.483 & 0.044 &  1.3 & 80.0 \cr\hline
\end{tabular}
