## 5 Results and Analysis
### Benchmark Suite  
Table 3 illustrates the selected sparse matrices in our benchmark suite. We have selected 26 matrices for the benchmarking. Fifteen of these matrices are selected based on the recommendations by [85], which are the most frequently used matrices by the researchers for SpMV and iterative solvers. The other included matrices have been widely used (see e.g., [67; 79]). All the selected matrices are from the University of Florida Sparse Matrix Collection [86]. The chosen matrices are from diverse applications that include computational fluid dynamics, bioengineering, thermal, quantum chemistry, circuit simulation, power and web search. Figure 6 indicates the normalized mean and standard deviation of the non zeros per row for the matrices in our Benchmark suite. The red dots in the figure indicates the normalized mean and the bars indicate the normalized standard deviation. We can observe the irregularity in the number of non-zeros per row for these selected matrices. The high standard deviation for most of the matrices indicates the challenge in designing a uniform storage format and SpMV algorithm.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Struct** & **Matrix** & **Rows** & **Columns** & \(nmz\) & **Density (\%)** & **Symmetry** & **Problem Domain** \\ \hline  & 12 month1 & 12 471 & 872 622 & 22 624 727 & \(2.08\times 10^{-1}\) & unsymmetric & undir. bipartite graph \\ \hline \hline
**1** & _amazon312_ & 400 727 & 400 727 & 3 200 440 & \(1.99\times 10^{-3}\) & unsymmetric & directed graph \\ \hline \hline
**1** & _bundle\_adj_ & 513 351 & 513 351 & 20 207 907 & \(7.66\times 10^{-3}\) & symmetric & computer graphics \\ \hline \hline
**1** & _Freescale1_ & 3 428 755 & 3 428 755 & 18 920 347 & \(1.61\times 10^{-4}\) & unsymmetric & circuit simulation \\ \hline \hline
**1** & _FullChip_ & 2 987 012 & 2 987 012 & 26 621 990 & \(2.98\times 10^{-4}\) & unsymmetric & circuit simulation \\ \hline \hline
**1** & _hollywood-2009_ & 1 139 905 & 1 139 905 & 57 515 616 & \(4.43\times 10^{-3}\) & symmetric & undirected graph \\ \hline
**1** & _in-2004_ & 1 382 908 & 1 382 908 & 16 917 053 & \(8.85\times 10^{-4}\) & unsymmetric & directed graph \\ \hline
**1** & _mouse\_gene_ & 45 101 & 45 101 & 14 506 196 & \(7.13\times 10^{-1}\) & symmetric & undir. weighted graph \\ \hline
**1** & _nil4284_ & 4284 & 1 096 894 & 11 284 032 & \(2.40\times 10^{-1}\) & unsymmetric & linear programming \\ \hline
**1** & _RM07R_ & 381 689 & 381 689 & 37 464 962 & \(2.57\times 10^{-2}\) & unsymmetric & Computational Fluid Dynamics (CFD) \\ \hline
**1** & _spl\_004_ & 10 203 & 321 696 & 46 168 124 & \(1.41\times 10^{0}\) & unsymmetric & linear programming \\ \hline
**1** & _thermal2_ & 1 228 045 & 1 228 045 & 4 904 179 & \(3.25\times 10^{-4}\) & symmetric & thermal \\ \hline
**1** & _TSOPF\_RS\_b2383_ & 38 120 & 38 120 & 16 171 169 & \(1.11\times 10^{0}\) & unsymmetric & power network \\ \hline
**1** & _wb-edu_ & 9 845 725 & 9 845 725 & 57 156 537 & \(5.90\times 10^{-5}\) & unsymmetric & directed graph \\ \hline
**1** & _Zd\_lac2_ & 22 835 & 22 835 & 1 642 833 & \(3.15\times 10^{-1}\) & unsymmetric & chemical simulation \\ \hline
**1** & _llr71c_ & 70 304 & 70 304 & 1 528 092 & \(3.09\times 10^{-2}\) & unsymmetric & chemical simulation \\ \hline
**1** & _bundle1_ & 10 581 & 10 581 & 770 811 & \(0.68\times 10^{0}\) & symmetric & computer graphics \\ \hline
**1** & _thermomed\_TK_ & 102 158 & 102 158 & 711 558 & \(6.81\times 10^{-3}\) & symmetric & thermal \\ \hline \hline \end{tabular}
\end{table}
Table 3: Benchmark dataset: 26 matrices.