### Table 1: Measured computation times showing relative processor speeds.

1997

Cited by 6

### Table 7: Total time to compute L in seconds running on 1, 2, 4, 8, and 16 processors and the speed-up in the average time to compute one factorization L on 2, 4, 8, and 16 processors.

"... In PAGE 25: ... Indeed Table 6 to Table 9 show the total time to perform di erent tasks within the interior-point algorithm. In Table 6, Table7 , and Table 8 the speed- up is reported with respect to computation of ADAT and L. It should be noted that due to that the number of iterations varies for the same problem with the number of processors employed, then the speed-up is reported as the speed-up in the average time per factorization.... In PAGE 25: ... Indeed, even in the case of 16 processors a satisfactory speed-up is obtained for computation of ADAT and L for the majority of the problems. Moreover, by comparing the results in Table 6 and Table7 it can be seen that the speed-up obtained, when computing L is slightly better than when computing ADAT . Note that except for the two problems mod2 and pilot87, then the speed-up obtained is better for the computation of L alone than for computing both L and ADAT when using 16 processors.... ..."

### Table 2: Sample values of for various representative combinations of processor and network speeds. A computation to communication ratio of r = 0:5 Flops/bit[23] is assumed. Processor Speed Processor Network Channel Network Channel = (D=r)t

"... In PAGE 10: ... For deriving representative values of in current and future systems, we consider predictions made by Patterson [20]. As shown in Table2 , for a computation to communi- cation ratio r = 0:5 Flops/bit the values of broadly lie in the range of 0.... ..."

### Table 1 Measured computation times showing relative processor speeds Name Nala Bluegrass Dancer Donner Vixen Rudolph Zazu Simba

1998

### TABLE II Sample values of for various representative combinations of processor and Interconnection Link speeds. A computation to communication ratio of r = 0:5 FLOPs/bit[20] is assumed.

1996

Cited by 12

### Table 6: Total time to compute L and ADAT in seconds running on 1, 2, 4, 8, and 16 processors and speed-up for average time per factorization for 2, 4, 8, and 16 processors.

"... In PAGE 25: ... Next we will investigate speed-up for di erent computational tasks within the interior- point algorithm. Indeed Table6 to Table 9 show the total time to perform di erent tasks within the interior-point algorithm. In Table 6, Table 7, and Table 8 the speed- up is reported with respect to computation of ADAT and L.... In PAGE 25: ... Indeed Table 6 to Table 9 show the total time to perform di erent tasks within the interior-point algorithm. In Table6 , Table 7, and Table 8 the speed- up is reported with respect to computation of ADAT and L. It should be noted that due to that the number of iterations varies for the same problem with the number of processors employed, then the speed-up is reported as the speed-up in the average time per factorization.... In PAGE 25: ... It should be noted that due to that the number of iterations varies for the same problem with the number of processors employed, then the speed-up is reported as the speed-up in the average time per factorization. It is evident from a comparison of the results in Table 5 with the results in Table6 that the computation of ADAT and L gives a much better speed-up than the interior-point algorithm as a whole. Indeed, even in the case of 16 processors a satisfactory speed-up is obtained for computation of ADAT and L for the majority of the problems.... In PAGE 25: ... Indeed, even in the case of 16 processors a satisfactory speed-up is obtained for computation of ADAT and L for the majority of the problems. Moreover, by comparing the results in Table6 and Table 7 it can be seen that the speed-up obtained, when computing L is slightly better than when computing ADAT . Note that except for the two problems mod2 and pilot87, then the speed-up obtained is better for the computation of L alone than for computing both L and ADAT when using 16 processors.... ..."

### Table 3: Computing times and speed-ups obtained in runs with di erent number of processors, for two grids on a the CRAY T3D (only chemistry is used).

### Table 3 shows the speed-up of the parallel algorithms computed as the ratio between the parallel execution time on pp pp processors and the serial execution time. The table reports acceptable speed-ups for 4 and 9 processors; the speed-up is however quite low for 16 processors due to the small size of the problems evaluated.

### Table 6 Speedups with Di erent Processor Speeds

in Evaluation of Release Consistent Software Distributed Shared Memory on Emerging Network Technology

1992

"... In PAGE 11: ... We varied the processor speeds from 20 to 80 MHz. Table6 shows the variation in speedup for the 16 processor case when us- ing the lazy hybrid protocol in the case of Water, Jacobi and TSP, and the 8 processor case for Cholesky. For Ja- cobi and TSP, the variations are negligible because the low message counts for these programs results in little variation in the computation to communication ratio.... ..."