\documentclass[10pt]{article} \usepackage{longtable} \usepackage{xcolor} \newcommand{\blu}{ \color{blue} } \newcommand{\red}{ \color{red} } \begin{document} \appendix \section{Comprehensive Computational Results} \label{s:ResultsALL} Tables \ref{supptab:all_large}, \ref{supptab:all_medium}, \ref{supptab:all_small}, and \ref{supptab:all_tiny} present exhaustive computational results for large (those requiring $\geq1$ hour of run time), medium (those requiring between 1 hour and 1 minute of run time), small (those requiring between 1 minute and $0.1$ seconds of run time) and tiny (those requiring less than $0.1$ seconds) instances, respectively. In each table, the first five columns give the name (or index from SJ database), dimension, number of nonzeros, MATLAB estimated condition number, and MATLAB estimated sparse norm in each matrix. Column 6 gives the run time of SPEX Left LU using the selected pivoting scheme tol 0. Lastly, columns 7 and 8 give the relative run time of Wiedemann and Lanczos, respectively. Note that those instances in which these algorithms seg-fault are indicated with {\bf \red SF} and those instances whose solutions were incorrect are indicated with bold red text. \begin{longtable}{|l|r|r|r|r|r|r|r|} \hline & & & & & & \multicolumn{2}{c|}{Relative Run Time} \\ \hline \multicolumn{1}{|c|}{Matrix Name} & \multicolumn{1}{c|}{n} & \multicolumn{1}{c|}{nnz} & \multicolumn{1}{c|}{Cond} & \multicolumn{1}{c|}{norm} & \multicolumn{1}{c|}{SPEX time (hr)} & \multicolumn{1}{c|}{Wiedemann} & \multicolumn{1}{c|}{Lanczos} \\ \hline \endhead 350 & 6774 & 33744 & 7.68E+13 & 1.26E+06 & 10.40 & 0.01 & 0.01 \\ 367 & 7337 & 156508 & 7.64E+13 & 1.83E+01 & 10.12 & 0.04 & 0.04 \\ 696 & 14454 & 147972 & 4.44E+12 & 5.31E+03 & 9.78 & {\bf \red SF} & {\bf \red SF} \\ 695 & 14454 & 147972 & 3.10E+12 & 5.31E+03 & 9.67 & {\bf \red SF} & {\bf \red SF} \\ 213 & 3402 & 130371 & 2.67E+16 & 3.98E+14 & 8.31 & 0.02 & 0.02 \\ 352 & 5773 & 71701 & 8.77E+12 & 1.29E+08 & 8.09 & 0.03 & 0.03 \\ 119 & 3251 & 65875 & 2.62E+16 & 1.27E+07 & 7.54 & 0.01 & 0.01 \\ 344 & 3363 & 99471 & 4.08E+13 & 3.79E+09 & 7.37 & 0.02 & 0.02 \\ 337 & 5321 & 65693 & 2.10E+13 & 4.68E+06 & 6.74 & 0.02 & 0.02 \\ 117 & 3973 & 79077 & 1.49E+19 & 1.28E+02 & 6.51 & 0.02 & 0.02 \\ 346 & 7055 & 30082 & 1.65E+12 & 4.02E+02 & 6.35 & 0.03 & 0.03 \\ 347 & 7055 & 30082 & 6.34E+17 & 4.02E+02 & 6.09 & {\bf \red *0.02} & {\bf \red *0.02} \\ 140 & 3937 & 25407 & 1.04E+17 & 3.27E+11 & 5.06 & 0.01 & 0.01 \\ 221 & 4257 & 37465 & 2.52E+16 & 1.46E+02 & 4.50 & {\bf \red *0.01} & {\bf \red *0.01} \\ 222 & 4257 & 37465 & 2.52E+16 & 1.46E+02 & 4.49 & {\bf \red *0.01} & {\bf \red *0.01} \\ 223 & 4257 & 37465 & 1.21E+19 & 1.46E+02 & 4.49 & {\bf \red *0.01} & {\bf \red *0.01} \\ 142 & 3937 & 25407 & 1.04E+17 & 3.27E+11 & 4.41 & 0.01 & 0.01 \\ 341 & 2880 & 18229 & 9.74E+13 & 1.39E+04 & 4.25 & 0.01 & 0.01 \\ 349 & 4101 & 82682 & 1.44E+13 & 1.34E+01 & 3.54 & 0.03 & 0.04 \\ pilot87.pre & 1540 & 30916 & Inf & Inf & 2.70 & 0.01 & 0.01 \\ 118 & 2568 & 75628 & 4.01E+15 & 1.26E+10 & 2.18 & 0.04 & 0.04 \\ pilot87 & 1625 & 31396 & Inf & Inf & 1.85 & 0.01 & 0.01 \\ gen4 & 375 & 8919 & 8.43E+236 & Inf & 1.25 & 0.01 & 0.01 \\ 217 & 4720 & 20042 & 3.51E+48 & 1.89E+02 & 1.16 & 0.06 & 0.06 \\ self & 924 & 157411 & 1.20E+07 & 1.57E+11 & 1.15 & 0.02 & 0.02 \\ gen4.pre & 367 & 9322 & Inf & Inf & 1.12 & 0.01 & 0.01 \\ \hline \caption{Comprehensive Results: Large Instances} \small \centering \label{supptab:all_large} \end{longtable} \begin{longtable}{|l|r|r|r|r|r|r|r|} \hline & & & & & & \multicolumn{2}{c|}{Relative Run Time} \\ \hline \multicolumn{1}{|c|}{Matrix Name} & \multicolumn{1}{c|}{n} & \multicolumn{1}{c|}{nnz} & \multicolumn{1}{c|}{Cond} & \multicolumn{1}{c|}{Norm} & \multicolumn{1}{c|}{SPEX time (min)} & \multicolumn{1}{c|}{Wiedemann} & \multicolumn{1}{c|}{Lanczos} \\ \hline \endhead slptsk & 2315 & 34430 & 4.35E+185 & NaN & 54.85 & 0.19 & 0.19 \\ gen1 & 329 & 11016 & Inf & Inf & 44.42 & 0.03 & 0.03 \\ 207 & 1919 & 32399 & 3.73E+18 & 2.92E+00 & 33.82 & 0.04 & 0.04 \\ 335 & 6747 & 29195 & 2.22E+18 & 5.41E+08 & 32.89 & 0.21 & 0.21 \\ 87 & 2500 & 12349 & 4.35E+17 & 9.83E+03 & 26.86 & 0.05 & 0.05 \\ pla8\_sig185 & 39835 & 196256 & 4.29E+09 & 1.04E+03 & 17.17 & 0.16 & 0.17 \\ 355 & 1409 & 42760 & 2.28E+13 & 2.67E+05 & 13.90 & 0.08 & 0.08 \\ 159 & 1050 & 26198 & 9.00E+15 & 2.10E+07 & 12.37 & 0.04 & 0.04 \\ pilot & 1132 & 16624 & 1.12E+175 & NaN & 10.04 & 0.03 & 0.03 \\ maros-r7 & 1350 & 31923 & 7.43E+06 & 3.99E+10 & 8.62 & 0.03 & 0.03 \\ 320 & 1733 & 22189 & 1.20E+13 & 1.18E+11 & 8.30 & 0.14 & 0.15 \\ stat96v4 & 3139 & 23752 & 9.62E+17 & 1.63E+21 & 6.47 & 0.17 & 0.17 \\ pla85900.nov21 & 40304 & 230558 & 5.46E+08 & 9.76E+02 & 6.17 & 0.49 & 0.50 \\ 153 & 765 & 24382 & 1.67E+14 & 1.35E+17 & 5.68 & 0.08 & 0.08 \\ 58 & 3083 & 11767 & 2.30E+21 & 1.21E+09 & 5.62 & 0.23 & 0.23 \\ momentum3 & 3254 & 15159 & Inf & Inf & 5.36 & 0.31 & 0.31 \\ jendrec1 & 1779 & 34196 & 9.54E+217 & NaN & 4.12 & 3.64 & 3.64 \\ 296 & 1258 & 7682 & 1.03E+13 & 2.05E+07 & 3.99 & 0.07 & 0.06 \\ brd14051 & 16360 & 180847 & 2.96E+08 & 2.74E+02 & 3.07 & 0.41 & 0.41 \\ fome13 & 24884 & 70839 & 7.99E+15 & 4.02E+11 & 3.07 & 0.34 & 0.34 \\ 240 & 1000 & 1000000 & 1.61E+21 & 6.46E+00 & 2.69 & {\bf \red *6.22} & {\bf \red *6.09} \\ 236 & 1000 & 1000000 & 3.25E+19 & 3.23E+00 & 2.38 & {\bf \red *6.53} & {\bf \red *6.73} \\ mod2.pre & 4422 & 12914 & 3.72E+246 & NaN & 2.29 & 1.48 & 1.48 \\ 260 & 1000 & 1000000 & 1.15E+14 & 5.36E-01 & 2.23 & {\bf \red *7.04} & {\bf \red *7.03} \\ world & 4261 & 12190 & 5.65E+241 & NaN & 2.18 & 1.26 & 1.27 \\ l30 & 2492 & 12653 & 1.73E+08 & 2.61E+09 & 2.15 & 0.21 & 0.22 \\ 340 & 8765 & 42471 & 6.15E+14 & 1.00E+15 & 1.82 & 11.26 & 11.13 \\ cont11\_l & 58936 & 179556 & 3.65E+26 & 7.37E+00 & 1.80 & 9.68 & 9.67 \\ mod2 & 4435 & 12985 & 1.38E+223 & NaN & 1.74 & 1.77 & 1.79 \\ 309 & 2837 & 10967 & 5.85E+12 & 7.41E+05 & 1.58 & 0.82 & 0.81 \\ 314 & 2836 & 10965 & 5.85E+12 & 7.41E+05 & 1.58 & 0.81 & 0.83 \\ 232 & 1000 & 1000000 & 1.85E+21 & 8.11E-01 & 1.44 & {\bf \red *10.48} & {\bf \red *10.32} \\ gen2 & 328 & 8894 & 1.84E+11 & 4.51E+18 & 1.35 & 0.04 & 0.04 \\ scfxm1-2r-256 & 11812 & 44985 & 3.12E+12 & 2.84E+08 & 1.11 & 2.95 & 2.94 \\ \hline \caption{Comprehensive Results: Medium Instances} \small \centering \label{supptab:all_medium} \end{longtable} \begin{longtable}{|l|r|r|r|r|r|r|r|} \hline & & & & & & \multicolumn{2}{c|}{Relative Run Time} \\ \hline \multicolumn{1}{|c|}{Matrix Name} & \multicolumn{1}{c|}{n} & \multicolumn{1}{c|}{nnz} & \multicolumn{1}{c|}{Cond} & \multicolumn{1}{c|}{Norm} & \multicolumn{1}{c|}{SPEX time (s)} & \multicolumn{1}{c|}{Wiedemann} & \multicolumn{1}{c|}{Lanczos} \\ \hline \endhead nemswrld & 2205 & 13323 & NaN & Inf & 53.50 & 0.34 & 0.34 \\ cont4 & 2802 & 11862 & 3.85E+05 & 3.98E+03 & 44.81 & 0.28 & 0.29 \\ rat5 & 902 & 12026 & 4.19E+06 & 7.48E+05 & 40.77 & 0.10 & 0.10 \\ nug30 & 14681 & 45627 & 1.06E+06 & 7.88E+00 & 37.07 & 0.68 & 0.63 \\ nug20 & 7733 & 31455 & 8.84E+07 & 7.26E+00 & 35.20 & 0.26 & 0.28 \\ stat96v1 & 5013 & 20325 & 6.35E+32 & 8.22E+20 & 34.16 & 0.45 & 0.44 \\ stat96v2 & 12928 & 48009 & 1.06E+13 & 1.32E+10 & 32.85 & 1.07 & 1.08 \\ 210 & 1484 & 6110 & 5.57E+17 & 1.26E+16 & 29.97 & 0.95 & 0.96 \\ pla33810 & 18940 & 123445 & 1.05E+08 & 2.20E+02 & 29.57 & 1.64 & 1.61 \\ stat96v3 & 13485 & 49917 & 3.93E+12 & 6.98E+09 & 27.62 & 1.29 & 1.31 \\ nug15 & 5486 & 24736 & 2.41E+07 & 7.73E+00 & 26.99 & 0.19 & 0.17 \\ pilot.ja & 567 & 3781 & Inf & Inf & 25.13 & 0.32 & 0.31 \\ model10 & 1341 & 6403 & 1.71E+164 & Inf & 24.62 & 0.50 & 0.50 \\ rat7a & 641 & 10542 & 1.38E+20 & 5.06E+05 & 18.88 & 0.12 & 0.13 \\ d2q06c & 1047 & 5717 & 1.82E+188 & Inf & 18.27 & 0.48 & 0.48 \\ 128 & 760 & 5739 & 1.12E+16 & 3.10E+08 & 18.26 & 0.29 & 0.29 \\ d15112 & 9197 & 47335 & 2.33E+18 & 2.25E+11 & 17.95 & 2.21 & 2.23 \\ 141 & 511 & 2796 & 6.37E+15 & 4.21E+10 & 16.60 & 0.17 & 0.16 \\ 144 & 511 & 2796 & 6.37E+15 & 4.21E+10 & 16.49 & 0.17 & 0.17 \\ progas & 1167 & 6500 & 8.15E+103 & 6.78E+100 & 14.19 & 0.91 & 0.91 \\ co9 & 2287 & 13481 & 2.32E+49 & 1.56E+42 & 13.06 & 0.98 & 0.99 \\ stat96v5 & 812 & 3795 & 1.42E+63 & 3.93E+64 & 13.00 & 1.11 & 1.11 \\ l30.pre & 1199 & 6030 & 1.79E+06 & 2.61E+09 & 12.56 & 0.24 & 0.24 \\ scfxm1-2b-64 & 5966 & 22682 & 1.30E+12 & 2.84E+08 & 12.11 & 3.96 & 3.94 \\ 158 & 416 & 8562 & 2.41E+25 & 2.54E+03 & 12.08 & 0.24 & 0.25 \\ scfxm1-2r-128 & 5671 & 21943 & 1.64E+12 & 2.84E+08 & 11.80 & 3.89 & 3.85 \\ 332 & 4101 & 36879 & 6.72E+20 & 2.02E+06 & 11.67 & 12.63 & 12.65 \\ NSR8K & 5387 & 46157 & 2.64E+07 & 2.06E+03 & 11.62 & 0.66 & 0.66 \\ qap12 & 2740 & 12014 & 2.46E+07 & 6.84E+00 & 10.96 & 0.11 & 0.11 \\ newman2 & 468 & 7917 & 1.39E+225 & Inf & 10.85 & 0.23 & 0.23 \\ watson\_1 & 5729 & 14544 & 7.98E+58 & 9.72E+55 & 9.00 & 10.75 & 10.84 \\ 209 & 415 & 2779 & 1.04E+18 & 6.47E+00 & 8.66 & 0.23 & 0.25 \\ pilotnov & 549 & 3337 & 2.82E+264 & NaN & 8.64 & 0.54 & 0.54 \\ 239 & 500 & 250000 & 3.27E+20 & 6.46E+00 & 8.38 & {\bf \red *15.04} & {\bf \red *15.55} \\ momentum2 & 2113 & 6516 & 2.52E+39 & 1.88E+37 & 8.35 & 1.10 & 1.08 \\ 238 & 200 & 40000 & 8.07E+19 & 6.46E+00 & 8.32 & 0.68 & 0.68 \\ pilot4 & 289 & 2805 & Inf & Inf & 7.75 & 0.57 & 0.57 \\ 235 & 500 & 250000 & 1.01E+19 & 3.23E+00 & 7.52 & {\bf \red *16.55} & {\bf \red *16.30} \\ 231 & 500 & 250000 & 8.95E+20 & 8.11E-01 & 7.43 & {\bf \red *15.82} & {\bf \red *16.21} \\ dbic1 & 4795 & 23403 & 1.04E+11 & 4.53E+06 & 7.18 & 1.05 & 1.04 \\ perold & 440 & 2584 & 4.45E+256 & NaN & 7.13 & 0.56 & 0.56 \\ 259 & 500 & 250000 & 1.65E+14 & 5.36E-01 & 7.12 & {\bf \red *16.58} & {\bf \red *16.49} \\ watson\_1.pre & 4642 & 12991 & 3.44E+58 & 9.72E+55 & 7.05 & 10.03 & 9.87 \\ cont1\_l & 1070 & 4649 & 1.22E+09 & 2.51E+05 & 6.23 & 0.47 & 0.46 \\ scfxm1-2r-96 & 4504 & 17205 & 1.35E+12 & 2.84E+08 & 6.22 & 4.32 & 4.30 \\ 126 & 1220 & 5884 & 1.06E+14 & 9.34E+00 & 5.99 & 2.16 & 2.19 \\ 291 & 1220 & 5860 & 1.80E+13 & 8.78E+00 & 5.91 & 2.14 & 2.16 \\ 212 & 882 & 3354 & 7.98E+16 & 6.69E+12 & 5.87 & 1.52 & 1.51 \\ 125 & 1220 & 5892 & 1.58E+17 & 2.88E+00 & 5.69 & 2.25 & 2.24 \\ nug12 & 2736 & 12037 & 2.25E+07 & 6.97E+00 & 5.62 & 0.22 & 0.23 \\ 288 & 1220 & 5852 & 2.74E+13 & 1.23E+01 & 5.55 & 2.35 & 2.29 \\ pcb3038 & 3588 & 46560 & 2.00E+06 & 1.55E+02 & 5.41 & 0.72 & 0.72 \\ 127 & 1220 & 5855 & 6.25E+14 & 3.70E+02 & 5.39 & 2.36 & 2.38 \\ model11 & 2039 & 7606 & 1.40E+32 & 3.38E+29 & 5.28 & 1.11 & 1.10 \\ 294 & 1220 & 5892 & 2.74E+13 & 1.23E+01 & 5.20 & 2.49 & 2.43 \\ 287 & 1220 & 5888 & 4.14E+13 & 1.63E+01 & 4.65 & 2.78 & 2.79 \\ 289 & 1220 & 5884 & 1.42E+13 & 4.95E+00 & 4.39 & 2.87 & 2.86 \\ 292 & 1220 & 5888 & 3.45E+13 & 2.02E+01 & 4.29 & 2.94 & 2.93 \\ nemspmm2 & 949 & 6478 & 2.61E+222 & Inf & 4.24 & 1.02 & 1.02 \\ 211 & 768 & 2934 & 1.29E+17 & 1.36E+13 & 4.01 & 1.69 & 1.67 \\ 293 & 1220 & 5892 & 1.58E+13 & 8.37E+00 & 3.40 & 3.65 & 3.69 \\ stormg2\_1000.pre & 13926 & 32547 & 2.13E+11 & 2.59E+05 & 3.27 & 31.02 & 31.19 \\ 124 & 1220 & 5892 & 2.24E+34 & 2.87E+00 & 2.91 & 3.98 & 3.92 \\ stormg2\_1000 & 14075 & 32597 & 3.77E+09 & 1.05E+04 & 2.90 & 32.90 & 32.98 \\ 152 & 180 & 2659 & 3.59E+17 & 2.04E+19 & 2.60 & 0.32 & 0.32 \\ fome12 & 12652 & 35969 & 8.93E+05 & 4.65E+01 & 2.53 & 4.63 & 4.58 \\ nl & 890 & 2919 & 5.83E+293 & Inf & 2.46 & 3.32 & 3.33 \\ fnl4461 & 5044 & 46977 & 4.12E+06 & 2.35E+02 & 2.36 & 2.28 & 2.31 \\ model6 & 790 & 3425 & 5.17E+63 & 4.11E+61 & 2.35 & 1.22 & 1.21 \\ scfxm1-2r-64 & 1870 & 11122 & 8.23E+11 & 2.84E+08 & 2.31 & 4.92 & 4.93 \\ co5 & 928 & 6173 & 3.86E+185 & Inf & 2.26 & 2.21 & 2.20 \\ pla7397 & 5059 & 42683 & 8.55E+06 & 3.36E+02 & 2.17 & 2.11 & 2.13 \\ nemspmm1 & 982 & 5023 & 4.94E+23 & 1.59E+20 & 2.12 & 1.30 & 1.30 \\ 315 & 2053 & 18447 & 6.71E+16 & 2.03E+04 & 2.09 & 16.27 & 16.18 \\ rl11849 & 6769 & 40885 & 1.21E+08 & 1.92E+02 & 2.09 & 3.40 & 3.36 \\ d18512 & 10815 & 55880 & 8.61E+05 & 2.09E+02 & 1.99 & 7.06 & 7.00 \\ cq9 & 1187 & 5786 & 4.94E+165 & Inf & 1.52 & 3.14 & 3.13 \\ qap10 & 1510 & 6381 & 4.45E+06 & 6.13E+00 & 1.49 & 0.21 & 0.20 \\ de080285 & 368 & 1493 & 1.06E+78 & 1.36E+79 & 1.41 & 1.12 & 1.11 \\ rail4284 & 2463 & 11802 & 3.58E+04 & 7.23E+00 & 1.37 & 0.63 & 0.63 \\ pilot.we & 554 & 2367 & 5.11E+137 & 4.03E+133 & 1.27 & 2.60 & 2.63 \\ newman & 334 & 2156 & 6.20E+233 & Inf & 1.24 & 0.97 & 0.98 \\ ge & 1675 & 4758 & 3.29E+130 & 7.56E+127 & 1.14 & 7.58 & 7.65 \\ rat1 & 452 & 2893 & 3.93E+27 & 2.26E+30 & 1.10 & 0.70 & 0.68 \\ dano3mip.pre & 1091 & 5239 & 3.46E+10 & 1.36E+05 & 1.08 & 0.41 & 0.41 \\ 342 & 10001 & 49999 & 4.17E+18 & 5.00E+03 & 0.98 & {\bf \red *846.53} & {\bf \red *845.32} \\ t0331-4l & 520 & 5034 & 2.75E+04 & 1.10E+01 & 0.91 & 0.25 & 0.25 \\ 132 & 216 & 812 & 8.10E+14 & 1.39E+00 & 0.89 & 0.48 & 0.44 \\ model5 & 492 & 2247 & 7.35E+109 & 1.03E+108 & 0.88 & 2.13 & 2.09 \\ dano3mip & 1135 & 5390 & 2.47E+10 & 1.36E+05 & 0.85 & 0.55 & 0.52 \\ grow22 & 434 & 4711 & 2.09E+17 & 4.39E+16 & 0.85 & 1.29 & 1.30 \\ rl5915 & 3853 & 28829 & 3.43E+06 & 1.03E+02 & 0.82 & 3.22 & 3.24 \\ model9 & 902 & 4361 & 3.90E+23 & 6.53E+20 & 0.75 & 2.31 & 2.31 \\ siena1 & 1265 & 11573 & 6.40E+05 & 7.85E+02 & 0.67 & 0.63 & 0.62 \\ fome11 & 6226 & 17749 & 6.31E+05 & 5.09E+01 & 0.64 & 4.35 & 4.28 \\ model7 & 646 & 2850 & 2.89E+137 & 2.87E+134 & 0.64 & 2.59 & 2.61 \\ rl5934 & 3773 & 23917 & 2.94E+06 & 1.11E+02 & 0.63 & 3.26 & 3.21 \\ nesm & 279 & 895 & 1.01E+127 & 1.12E+125 & 0.63 & 3.20 & 3.22 \\ model4 & 409 & 1898 & 9.08E+213 & NaN & 0.57 & 2.61 & 2.59 \\ de063155 & 313 & 1233 & 1.09E+95 & 6.12E+69 & 0.54 & 2.33 & 2.30 \\ lp22.pre & 1811 & 13146 & 3.89E+05 & 1.27E+01 & 0.52 & 1.44 & 1.36 \\ orna1 & 810 & 2842 & 2.66E+13 & 2.55E+15 & 0.51 & 3.36 & 3.38 \\ lp22 & 1796 & 13076 & 1.32E+05 & 1.29E+01 & 0.49 & 1.60 & 1.55 \\ scfxm1-2r-32 & 1447 & 5658 & 2.93E+11 & 2.84E+08 & 0.46 & 6.37 & 6.50 \\ 233 & 100 & 10000 & 1.69E+20 & 3.23E+00 & 0.44 & 1.66 & 1.71 \\ van & 7417 & 21681 & 4.24E+04 & 7.23E+00 & 0.44 & 7.33 & 7.27 \\ usa13509 & 3595 & 19919 & 2.89E+08 & 1.70E+02 & 0.43 & 6.23 & 6.11 \\ 237 & 100 & 10000 & 1.08E+19 & 6.46E+00 & 0.40 & 1.92 & 1.85 \\ arki001 & 160 & 893 & 4.46E+299 & Inf & 0.37 & 4.08 & 4.07 \\ 230 & 200 & 40000 & 9.06E+19 & 8.11E-01 & 0.37 & {\bf \red *15.47} & {\bf \red *15.07} \\ greenbeb & 713 & 3278 & 1.17E+25 & 9.16E+21 & 0.36 & 3.26 & 3.27 \\ 234 & 200 & 40000 & 1.74E+18 & 3.23E+00 & 0.35 & {\bf \red *15.54} & {\bf \red *16.51} \\ 280 & 430 & 1544 & 2.91E+13 & 2.00E+06 & 0.35 & 4.89 & 4.87 \\ 258 & 200 & 40000 & 1.40E+14 & 5.36E-01 & 0.35 & {\bf \red *15.23} & {\bf \red *15.24} \\ grow15 & 297 & 3614 & 1.65E+13 & 4.24E+16 & 0.34 & 1.62 & 1.60 \\ complex & 327 & 10738 & 9.05E+04 & 5.39E+01 & 0.33 & 0.44 & 0.43 \\ scfxm1-2r-27 & 1222 & 4753 & 5.08E+10 & 2.84E+08 & 0.33 & 6.63 & 6.65 \\ newman3 & 369 & 3662 & 1.58E+23 & 3.91E+19 & 0.30 & 1.45 & 1.47 \\ momentum1 & 932 & 2792 & 1.18E+146 & 2.49E+141 & 0.30 & 7.92 & 7.89 \\ dfl001 & 3271 & 9276 & 4.54E+05 & 4.33E+01 & 0.27 & 2.82 & 2.81 \\ dfl001.pre & 2097 & 6501 & 4.10E+05 & 3.99E+01 & 0.27 & 1.33 & 1.31 \\ stair & 324 & 3431 & 1.27E+19 & 4.02E+15 & 0.27 & 1.18 & 1.15 \\ stocfor3 & 1782 & 4562 & 2.03E+31 & 3.50E+27 & 0.26 & 23.01 & 22.94 \\ large000 & 823 & 2282 & 1.39E+31 & 1.02E+34 & 0.25 & 14.33 & 14.49 \\ ulevimin & 697 & 1879 & 8.89E+103 & 5.41E+96 & 0.24 & 5.86 & 5.95 \\ t1717 & 549 & 3657 & 1.89E+04 & 7.40E+00 & 0.24 & 0.40 & 0.44 \\ de063157 & 282 & 1102 & 1.10E+97 & 6.45E+77 & 0.24 & 4.26 & 4.30 \\ car4 & 122 & 4384 & 1.30E+14 & 4.51E+15 & 0.22 & 1.35 & 1.35 \\ greenbea & 664 & 2706 & 2.17E+38 & 2.38E+32 & 0.21 & 4.38 & 4.46 \\ pcb3000 & 3058 & 27446 & 5.01E+04 & 6.24E+01 & 0.21 & 6.87 & 6.91 \\ 25fv47 & 416 & 2061 & 1.42E+35 & 7.33E+32 & 0.21 & 2.01 & 1.94 \\ 277 & 183 & 1069 & 2.69E+13 & 1.15E+09 & 0.20 & {\bf \red *1.46} & {\bf \red *1.45} \\ stp3d & 10642 & 25936 & 4.12E+05 & 4.28E+00 & 0.20 & 28.09 & 27.93 \\ trento1 & 1070 & 10010 & 1.54E+05 & 6.57E+02 & 0.19 & 1.23 & 1.23 \\ cq5 & 570 & 2615 & 1.05E+164 & Inf & 0.19 & 5.51 & 5.48 \\ dc1l & 851 & 5171 & 1.68E+05 & 9.70E+02 & 0.18 & 0.72 & 0.72 \\ gran & 284 & 1958 & 7.38E+32 & 1.25E+27 & 0.17 & 3.00 & 3.00 \\ dg012142 & 892 & 3627 & 9.32E+07 & 2.13E+04 & 0.15 & 2.51 & 2.42 \\ nug08 & 732 & 3004 & 2.49E+05 & 5.71E+00 & 0.15 & 0.42 & 0.43 \\ watson\_2 & 1011 & 2703 & 7.02E+42 & 1.78E+40 & 0.15 & 10.16 & 10.25 \\ dc1c & 808 & 4698 & 1.26E+06 & 9.63E+02 & 0.14 & 0.79 & 0.81 \\ scfxm1-2r-16 & 752 & 2962 & 1.94E+10 & 2.84E+08 & 0.13 & 5.99 & 6.02 \\ air04 & 630 & 4187 & 1.29E+04 & 8.67E+00 & 0.12 & 0.55 & 0.55 \\ aa01 & 630 & 4187 & 1.29E+04 & 8.67E+00 & 0.12 & 0.57 & 0.56 \\ nemsemm2 & 789 & 2440 & 1.78E+124 & 1.79E+123 & 0.12 & 16.53 & 16.46 \\ scfxm1-2b-16 & 784 & 2975 & 3.37E+10 & 2.84E+08 & 0.12 & 6.69 & 6.76 \\ pf2177 & 406 & 1772 & 9.40E+03 & 4.65E+00 & 0.12 & 0.27 & 0.28 \\ dolom1 & 806 & 5681 & 3.47E+05 & 2.27E+03 & 0.11 & 1.11 & 1.13 \\ model3 & 310 & 1417 & 3.11E+95 & 6.44E+93 & 0.10 & 3.27 & 3.25 \\ \hline \caption{Comprehensive Results: Small Instances} \small \centering \label{supptab:all_small} \end{longtable} \begin{longtable}{|l|r|r|r|r|r|r|r|} \hline & & & & & & \multicolumn{2}{c|}{Relative Run Time} \\ \hline \multicolumn{1}{|c|}{Matrix Name} & \multicolumn{1}{c|}{n} & \multicolumn{1}{c|}{nnz} & \multicolumn{1}{c|}{Cond} & \multicolumn{1}{c|}{Norm} & \multicolumn{1}{c|}{SPEX Left LU time (ms)} & \multicolumn{1}{c|}{Wiedemann} & \multicolumn{1}{c|}{Lanczos} \\ \hline \endhead ds & 647 & 12193 & 1.01E+04 & 2.08E+01 & 9.85 & 2.83 & 2.68 \\ ch & 393 & 1304 & 4.36E+110 & 3.12E+106 & 9.21 & 8.74 & 8.84 \\ nug07 & 450 & 1780 & 5.45E+04 & 5.28E+00 & 8.92 & 0.80 & 0.31 \\ 229 & 100 & 10000 & 6.48E+18 & 8.11E-01 & 8.51 & {\bf \red *8.37} & {\bf \red *8.24} \\ cr42 & 304 & 608 & 1.52E+35 & 1.86E+84 & 8.10 & 40.60 & 40.68 \\ 143 & 131 & 536 & 1.49E+15 & 9.77E+09 & 8.05 & 2.95 & 1.90 \\ delf000 & 593 & 1606 & 1.27E+18 & 1.44E+20 & 7.23 & 18.52 & 18.91 \\ 257 & 100 & 10000 & 3.09E+14 & 5.36E-01 & 6.99 & {\bf \red *9.84} & {\bf \red *10.18} \\ air06 & 562 & 3420 & 1.07E+04 & 9.00E+00 & 6.79 & 0.60 & 0.61 \\ protfold & 574 & 2562 & 8.36E+03 & 6.50E+00 & 6.71 & 0.66 & 0.65 \\ pldd000b & 537 & 1448 & 9.92E+18 & 1.27E+22 & 6.59 & 16.57 & 16.59 \\ 279 & 261 & 2319 & 7.54E+16 & 2.03E+04 & 6.46 & 9.95 & 9.87 \\ msc98-ip & 2897 & 10006 & 1.63E+07 & 4.26E+02 & 6.32 & 21.45 & 21.58 \\ l9 & 241 & 1381 & 7.65E+21 & 1.74E+19 & 6.18 & 2.44 & 2.44 \\ model2 & 149 & 757 & 1.15E+112 & 4.60E+108 & 6.16 & 2.54 & 2.56 \\ pcb1000 & 1156 & 9955 & 2.28E+04 & 4.37E+01 & 6.15 & 3.06 & 3.11 \\ aa03 & 562 & 3420 & 1.07E+04 & 9.00E+00 & 5.79 & 0.72 & 0.71 \\ lpl1 & 2692 & 7211 & 8.18E+08 & 1.02E+04 & 5.16 & 16.99 & 17.30 \\ biella1 & 813 & 5726 & 2.72E+04 & 1.18E+01 & 5.03 & 2.78 & 2.76 \\ grow7 & 138 & 1744 & 8.45E+12 & 3.53E+16 & 4.91 & 2.86 & 2.83 \\ bg512142 & 560 & 2140 & 6.92E+06 & 1.95E+03 & 4.71 & 3.18 & 3.20 \\ 139 & 131 & 536 & 1.49E+15 & 9.77E+09 & 4.53 & 3.45 & 3.40 \\ rosen10 & 989 & 6916 & 2.01E+03 & 1.35E+03 & 4.23 & 10.79 & 10.86 \\ stormg2-125.pre & 1780 & 4138 & 1.96E+09 & 5.43E+04 & 4.04 & 35.78 & 35.58 \\ df2177 & 414 & 1825 & 4.61E+03 & 4.74E+00 & 3.96 & 1.99 & 0.60 \\ stormg2-125 & 1886 & 4372 & 2.63E+07 & 2.26E+03 & 3.94 & 39.34 & 39.82 \\ rosen2 & 431 & 4143 & 7.85E+02 & 3.19E+02 & 3.63 & 3.88 & 3.87 \\ degen3 & 744 & 5431 & 1.66E+04 & 2.00E+01 & 3.52 & 1.70 & 1.71 \\ 10teams & 177 & 885 & 1.12E+03 & 5.63E+00 & 3.50 & 0.87 & 0.81 \\ scsd8 & 247 & 655 & 9.59E+18 & 1.58E+17 & 3.44 & 5.35 & 5.26 \\ pds-80 & 9225 & 19432 & 1.12E+04 & 5.66E+00 & 3.36 & 115.71 & 115.40 \\ bas1lp & 502 & 6651 & 9.77E+04 & 9.80E+01 & 3.28 & 3.22 & 3.12 \\ pilot4i & 134 & 1220 & 1.50E+33 & 4.19E+28 & 3.15 & 4.41 & 4.41 \\ cycle & 284 & 878 & 1.46E+79 & 3.19E+75 & 2.99 & 6.23 & 5.80 \\ pds-100 & 8377 & 17555 & 1.79E+04 & 5.48E+00 & 2.97 & 109.88 & 108.16 \\ scfxm1-2r-8 & 403 & 1608 & 7.45E+09 & 2.84E+08 & 2.94 & 7.89 & 7.92 \\ air05 & 323 & 1789 & 2.79E+04 & 6.94E+00 & 2.87 & 1.90 & 0.62 \\ pds-60 & 7586 & 16067 & 8.18E+03 & 4.48E+00 & 2.56 & 104.72 & 104.84 \\ gosh & 379 & 1379 & 8.05E+27 & 4.51E+24 & 2.49 & 12.14 & 12.47 \\ pds-90 & 7914 & 16673 & 1.48E+04 & 4.13E+00 & 2.43 & 114.84 & 117.41 \\ pds-70 & 7822 & 16545 & 1.11E+04 & 5.84E+00 & 2.14 & 132.65 & 133.20 \\ maros & 289 & 1143 & 2.76E+14 & 2.54E+11 & 2.13 & 4.07 & 4.08 \\ ganges & 344 & 1123 & 4.19E+26 & 3.03E+25 & 2.01 & 10.46 & 9.90 \\ fast0507 & 401 & 1908 & 3.72E+03 & 6.99E+00 & 1.94 & 3.54 & 1.26 \\ bandm & 122 & 609 & 1.12E+27 & 1.05E+26 & 1.94 & 3.02 & 3.03 \\ pds-50 & 5962 & 12592 & 1.04E+04 & 3.49E+00 & 1.87 & 81.12 & 81.91 \\ rail507 & 413 & 2005 & 5.39E+03 & 6.85E+00 & 1.87 & 3.09 & 1.44 \\ 30\_70\_4.5\_0.95\_100 & 2754 & 8381 & 6.12E+03 & 4.34E+00 & 1.83 & 36.49 & 30.40 \\ baxter.pre & 470 & 1274 & 3.55E+94 & 8.48E+88 & 1.61 & 13.78 & 13.99 \\ modszk1 & 263 & 765 & 1.52E+21 & 1.25E+20 & 1.59 & 9.74 & 9.81 \\ 30\_70\_4.5\_0.95\_98 & 2451 & 7364 & 7.84E+03 & 4.35E+00 & 1.54 & 28.46 & 26.87 \\ 30\_70\_4.5\_0.5\_100 & 2098 & 6197 & 1.98E+03 & 4.28E+00 & 1.48 & 21.62 & 21.47 \\ d6cube & 223 & 1424 & 9.56E+05 & 4.24E+02 & 1.47 & 2.78 & 2.44 \\ rentacar & 327 & 1080 & 3.64E+05 & 1.01E+03 & 1.41 & 2.27 & 1.70 \\ qiulp & 603 & 1717 & 8.25E+10 & 1.31E+09 & 1.38 & 9.67 & 9.95 \\ nug06 & 267 & 1007 & 1.04E+04 & 4.81E+00 & 1.35 & 2.36 & 2.46 \\ qiu & 603 & 1717 & 5.99E+10 & 1.31E+09 & 1.33 & 10.16 & 9.95 \\ scfxm1-2c-4 & 233 & 965 & 5.92E+09 & 2.84E+08 & 1.23 & 6.22 & 6.34 \\ rosen1 & 217 & 2528 & 1.23E+03 & 5.80E+02 & 1.15 & 3.85 & 3.82 \\ pds-40 & 4028 & 8478 & 6.64E+03 & 3.02E+00 & 1.10 & 50.46 & 50.21 \\ bnl2 & 459 & 1488 & 1.22E+15 & 1.10E+12 & 1.07 & 20.38 & 20.21 \\ mitre & 801 & 2466 & 4.18E+05 & 2.81E+03 & 1.07 & 37.24 & 36.80 \\ pds-30 & 2643 & 5641 & 3.27E+03 & 3.04E+00 & 1.07 & 30.21 & 30.34 \\ rail516 & 268 & 936 & 1.31E+03 & 5.64E+00 & 0.98 & 4.05 & 3.70 \\ fome21 & 3291 & 7240 & 9.21E+03 & 3.18E+00 & 0.98 & 48.53 & 48.54 \\ south31 & 112 & 460 & 1.68E+265 & Inf & 0.95 & 12.15 & 11.65 \\ rail582 & 384 & 1387 & 4.55E+03 & 5.10E+00 & 0.93 & 7.41 & 1.87 \\ seymour & 537 & 1881 & 5.24E+03 & 5.81E+00 & 0.92 & 4.72 & 3.52 \\ scfxm1-2b-4 & 233 & 965 & 5.92E+09 & 2.84E+08 & 0.84 & 9.50 & 9.27 \\ sp97ar & 271 & 2400 & 2.40E+04 & 3.93E+01 & 0.82 & 5.84 & 3.53 \\ neos6 & 174 & 1580 & 3.33E+03 & 7.20E+01 & 0.82 & 4.64 & 5.31 \\ neos & 2342 & 5098 & 3.29E+04 & 5.88E+00 & 0.77 & 25.92 & 27.98 \\ r05 & 919 & 2717 & 4.06E+04 & 3.06E+01 & 0.75 & 12.87 & 12.91 \\ manna81 & 1392 & 2784 & 3.00E+00 & 2.00E+00 & 0.73 & 11.09 & 11.15 \\ p05 & 919 & 2717 & 4.06E+04 & 3.06E+01 & 0.67 & 14.18 & 14.56 \\ scfxm1-2r-4 & 233 & 965 & 5.92E+09 & 2.84E+08 & 0.65 & 12.17 & 12.22 \\ bnl1 & 223 & 824 & 3.34E+23 & 2.35E+20 & 0.65 & 13.63 & 13.63 \\ rosen8 & 264 & 1850 & 2.53E+02 & 8.87E+01 & 0.57 & 6.49 & 6.40 \\ scagr7-2r-864 & 680 & 1697 & 6.99E+06 & 3.42E+03 & 0.57 & 49.66 & 48.56 \\ sp98ar & 223 & 1782 & 1.69E+04 & 4.43E+01 & 0.55 & 10.46 & 4.20 \\ fome20 & 1718 & 3811 & 5.39E+03 & 3.14E+00 & 0.55 & 27.11 & 26.91 \\ scrs8-2r-512 & 992 & 1984 & 1.92E+01 & 9.13E+00 & 0.54 & 29.88 & 29.67 \\ disctom & 192 & 565 & 5.92E+02 & 3.41E+00 & 0.52 & 3.41 & 3.34 \\ scfxm3 & 262 & 1005 & 1.67E+17 & 7.58E+13 & 0.52 & 18.62 & 18.57 \\ danoint & 196 & 790 & 2.11E+07 & 6.31E+03 & 0.51 & 9.36 & 4.55 \\ mzzv11 & 1098 & 3189 & 8.92E+05 & 2.46E+02 & 0.47 & 27.67 & 28.68 \\ 80bau3b & 154 & 396 & 3.31E+46 & 1.75E+45 & 0.46 & 17.53 & 17.59 \\ dbir2.pre & 281 & 1879 & 5.86E+06 & 1.10E+05 & 0.43 & 8.86 & 8.28 \\ capri & 138 & 507 & 3.72E+68 & 3.01E+65 & 0.43 & 23.65 & 23.64 \\ p010 & 839 & 2486 & 3.96E+04 & 3.06E+01 & 0.41 & 19.48 & 19.82 \\ degen2 & 217 & 1138 & 2.58E+03 & 1.15E+01 & 0.40 & 4.24 & 4.93 \\ scfxm2 & 178 & 658 & 1.67E+17 & 7.58E+13 & 0.37 & 12.38 & 12.29 \\ baxter & 256 & 697 & 3.06E+21 & 6.81E+15 & 0.37 & 15.96 & 15.58 \\ dbir1 & 154 & 845 & 4.54E+06 & 1.42E+06 & 0.35 & 17.05 & 17.36 \\ small000 & 140 & 383 & 6.77E+19 & 5.59E+23 & 0.34 & 29.03 & 29.08 \\ stormg2-27 & 449 & 1019 & 3.67E+06 & 1.77E+03 & 0.34 & 21.32 & 21.95 \\ roll3000 & 177 & 1101 & 2.19E+06 & 1.47E+03 & 0.34 & 18.49 & 15.37 \\ woodw & 168 & 589 & 1.44E+12 & 3.80E+10 & 0.32 & 19.94 & 20.28 \\ route & 339 & 1290 & 7.27E+08 & 2.03E+07 & 0.32 & 22.68 & 8.86 \\ nsct1 & 120 & 595 & 4.25E+06 & 7.67E+05 & 0.31 & 16.26 & 12.14 \\ neos.pre & 2080 & 4578 & 1.60E+04 & 5.86E+00 & 0.29 & 56.91 & 56.44 \\ mzzv42z & 787 & 2124 & 5.68E+05 & 2.01E+02 & 0.27 & 24.22 & 24.24 \\ crew1 & 127 & 861 & 7.82E+02 & 8.18E+00 & 0.27 & 7.76 & 11.03 \\ neos7 & 590 & 1434 & 1.46E+08 & 1.00E+06 & 0.26 & 54.87 & 55.02 \\ sgpf5y6 & 787 & 1870 & 6.24E+02 & 3.37E+00 & 0.22 & 34.46 & 12.04 \\ neos1 & 309 & 944 & 8.24E+02 & 4.83E+00 & 0.22 & 8.65 & 14.13 \\ neos11 & 365 & 1116 & 3.06E+03 & 5.06E+00 & 0.22 & 23.94 & 24.55 \\ nsct2.pre & 156 & 1140 & 3.84E+06 & 3.22E+05 & 0.21 & 18.44 & 7.87 \\ stocfor2 & 224 & 576 & 3.54E+26 & 1.50E+24 & 0.21 & 46.90 & 46.41 \\ scrs8-2r-256 & 416 & 832 & 1.92E+01 & 9.13E+00 & 0.20 & 38.34 & 12.82 \\ neos4 & 454 & 944 & 2.63E+08 & 5.59E+06 & 0.20 & 38.63 & 9.84 \\ blp-ar98 & 148 & 876 & 3.94E+03 & 9.40E+01 & 0.19 & 25.82 & 27.74 \\ dsbmip & 220 & 568 & 3.06E+46 & 2.19E+41 & 0.19 & 31.23 & 31.43 \\ sgpf5y6.pre & 755 & 1744 & 1.20E+02 & 3.22E+00 & 0.18 & 42.42 & 14.08 \\ neos823206 & 220 & 547 & 3.15E+05 & 2.24E+03 & 0.15 & 24.58 & 26.84 \\ sc205 & 184 & 487 & 1.18E+04 & 2.10E+01 & 0.15 & 21.46 & 21.34 \\ rosen7 & 127 & 649 & 8.23E+01 & 5.75E+01 & 0.14 & 39.64 & 14.59 \\ scrs8-2r-64 & 256 & 512 & 1.60E+05 & 1.41E+05 & 0.14 & 54.87 & 20.84 \\ pp08aCUTS & 131 & 332 & 1.44E+04 & 4.27E+02 & 0.13 & 14.12 & 12.34 \\ scorpion & 131 & 507 & 7.19E+06 & 2.00E+05 & 0.13 & 39.44 & 35.93 \\ lpl3 & 212 & 461 & 3.06E+02 & 2.61E+00 & 0.13 & 4.52 & 8.85 \\ p19 & 117 & 555 & 4.13E+05 & 4.37E+04 & 0.12 & 64.73 & 20.09 \\ iiasa & 113 & 262 & 6.06E+18 & 6.37E+17 & 0.12 & 28.25 & 28.10 \\ pds-20.pre & 370 & 851 & 1.07E+03 & 3.38E+00 & 0.12 & 25.30 & 23.88 \\ rd-rplusc-21 & 148 & 454 & 7.35E+16 & 4.38E+13 & 0.11 & 58.47 & 22.21 \\ neos19 & 228 & 487 & 7.19E+04 & 5.23E+01 & 0.11 & 59.49 & 35.86 \\ gesa2\_o & 102 & 214 & 6.47E+09 & 4.13E+08 & 0.11 & 51.49 & 38.52 \\ boeing1 & 122 & 415 & 7.36E+10 & 6.29E+07 & 0.11 & 46.04 & 47.62 \\ gesa3\_o & 148 & 365 & 1.73E+29 & 1.19E+26 & 0.10 & 52.90 & 32.00 \\ gesa3 & 134 & 336 & 1.73E+29 & 1.19E+26 & 0.10 & 69.71 & 27.82 \\ UMTS & 268 & 828 & 4.40E+20 & 3.24E+18 & 0.10 & 67.24 & 38.74 \\ scrs8 & 109 & 280 & 2.97E+27 & 8.93E+24 & 0.10 & 81.52 & 24.12 \\ scrs8-2r-128 & 192 & 384 & 1.92E+01 & 9.13E+00 & 0.10 & 19.11 & 24.55 \\ scrs8-2c-64 & 168 & 336 & 4.80E+01 & 2.66E+01 & 0.09 & 35.05 & 38.88 \\ ceria3d & 130 & 647 & 2.40E+04 & 1.09E+01 & 0.09 & 11.93 & 10.00 \\ stormg2-8 & 117 & 263 & 4.82E+05 & 1.77E+03 & 0.09 & 24.41 & 35.78 \\ nsct2 & 107 & 544 & 2.74E+06 & 2.40E+05 & 0.09 & 20.69 & 24.29 \\ mkc & 106 & 250 & 1.27E+06 & 2.89E+04 & 0.09 & 16.57 & 13.55 \\ scrs8-2r-32 & 128 & 256 & 4.16E+01 & 3.54E+01 & 0.09 & 26.58 & 46.92 \\ dbir2 & 157 & 784 & 1.71E+06 & 7.27E+04 & 0.09 & 30.31 & 33.46 \\ neos818918 & 265 & 678 & 4.29E+02 & 3.22E+00 & 0.09 & 26.79 & 25.53 \\ mkc1 & 106 & 250 & 1.27E+06 & 2.89E+04 & 0.08 & 13.77 & 15.81 \\ bienst1 & 102 & 253 & 7.61E+02 & 6.09E+00 & 0.06 & 11.97 & 9.59 \\ nug05 & 107 & 362 & 1.14E+03 & 4.15E+00 & 0.06 & 5.53 & 11.20 \\ dcmulti & 120 & 303 & 7.03E+03 & 6.26E+02 & 0.05 & 35.72 & 38.40 \\ \hline \caption{Comprehensive Results: Tiny Instances} \small \centering \label{supptab:all_tiny} \end{longtable} \end{document}