Tables of Results

These tables show the time to solution, parallel speed up, and parallel efficiency, where

$$Speed Up = \frac{Time_{serial}}{Time_{parallel}}$$

$$Efficiency = \frac{Speed Up}{N_{proc}}$$

Table 1: Time to Solution, Speed Up, and Efficiency from parallel execution on the SCL Alpha Cluster without dedicated access

	Time to Solution (seconds)
Size of Block	100000	1000000	2500000	5000000	10000000
$N_{proc}$
1	56.273	55.945	55.957	55.930	56.000
2	31.934	34.051	30.848	29.578	28.828
4	17.883	19.961	16.676	15.352	14.883
8	28.063	11.191	8.949	8.023	7.617
16	31.746	7.738	6.898	7.113	7.043
24	23.367	5.477	5.191	5.480	4.848

	Computed Speed Up
Size of Block	100000	1000000	2500000	5000000	10000000
$N_{proc}$
1	1.000	1.000	1.000	1.000	1.000
2	1.762	1.643	1.814	1.891	1.943
4	3.147	2.803	3.356	3.643	3.763
8	2.005	4.999	6.253	6.971	7.352
16	1.773	7.230	8.112	7.863	7.951
24	2.408	10.215	10.780	10.206	11.551

	Computed Efficiency
Size of Block	100000	1000000	2500000	5000000	10000000
$N_{proc}$
1	100.000	100.000	100.000	100.000	100.000
2	88.108	82.149	90.698	94.547	97.128
4	78.668	70.068	83.889	91.079	94.067
8	25.065	62.489	78.161	87.140	91.900
16	11.079	45.187	50.700	49.144	49.695
24	10.034	42.561	44.915	42.526	48.130