### Table 5: Numerical results for one way nonlinear multigrid

in SUMMARY

"... In PAGE 11: ...alculations. The numerical results are given in Tables 4 and 5. We obtain a speedup of 160 for the pseudo transient phase on four levels. As indicated in Table5 , the total execution times delivered are greater than the ones obtained with Bi-CGSTAB#2FGS. This latter algorithm seems therefore to be a preferrable linear smoother when using one way nonlinear multigrid.... ..."

### Table 3: Numerical results for one way nonlinear multigrid

in SUMMARY

"... In PAGE 10: ... On our workstation, the time stepping requires 15 seconds on the coarsest level as opposed to over 40 minutes on the #0Cnest, thus yielding a speedup of 166. Table3 breaks down the numerical results for the steady state Newton iterations. Note that the CPU time spent during the pseudo transient process has been included in the computation of the speedups presented in Table 3.... ..."

### Table 2 Numerical results for one way nonlinear multigrid

"... In PAGE 6: ...2mn#29. Table2 and Table 3 contain the results for the one waymultigrid and damped Newton multigrid methods. In these tables, the CPU time refers to the total time needed to solve #282#29, including the 20 preliminary time steps.... ..."

### Table 1 Numerical results for one way nonlinear multigrid during the time relaxation phase

### Table 1. Numerical examples of competitive ratios for some search and one-way trading algorithms (unknown duration).

2001

"... In PAGE 27: ... In this section we provide some numerical examples of competitive ratios attained by some of the algorithms discussed so far. Consider Table1 . Clearly, the optimal threat-based algorithm for the unknown duration case with m and M known is always significantly better than all other algorithms.... ..."

Cited by 22

### Table 1 which compares the actual and the estimated skeleton proportion in both numerical and graphical ways. The first column indicates the skeleton segment ID. The second column and third column show the skeleton proportion of that skeleton segment. The skeleton proportion is calculated by comparing its length to the sum of all skeleton lengths. The fourth column shows the difference between the estimated and the actual proportion. The last column compares the skeleton proportion in an intuitive way: the red skeleton with blue joints is the actual skeleton model while the green skeleton with black joints shows the estimation.

"... In PAGE 7: ... Table1 . Skeleton proportion estimation It can be easily seen from Table 1 that the estimated skeleton proportion resembles the actual skeleton proportion very closely.... In PAGE 7: ...Table 1. Skeleton proportion estimation It can be easily seen from Table1 that the estimated skeleton proportion resembles the actual skeleton proportion very closely. The errors between the estimation and the actual skeleton model are very small in lower hierarchical levels but increase in higher levels.... ..."

### Table 1. The results of ?(1;2)(n) calculations ( ?(n) = R 1 0 dxxnP (z)) performed in di erent ways, exact numerical results from [15] and approx- imation obtained from P (z; A; ?3) both numerical and analytical exact results are emphasized by the bold print.

"... In PAGE 7: ... But these contributions do not numerically dominate for real numbers of avours Nf = 4; 5; 6. That may be veri ed by comparing the total nu- merical results for the 2{ and 3{loop AD apos;s of composite operators (ADCO) presented in [16] with their Nf-leading terms (see ADCO in Table1 ). There- fore, to obtain a satisfactory agreement at least with the second order results, one should take into account the contribution from subleading Nf-terms.... In PAGE 8: ... The expansion of kernel P (1)(z; A; ) generates partial kernels a2 sP(1)(z); a3 sP(2)(z); : : : which in their turn produce ADCO a2 s ?(1)(n); a3 s ?(2)(n); : : : according to the relation ?(n) = R 1 0 dzznP (z). These elements of ADCO and a few numerical exact results from [16] are collected in Table1 , let us compare them: (i) we consider there the contribution to the coe cient ?(1)(n) which is generated by the gluon loops and associated with Casimirs CF CA=2, the C2 F {term is missed, but its contribution is numerically insigni cant. It is seen that in this order the CF CA{terms are rather close to exact values (the accuracy is about 10% for n gt; 2) and our approximation works rather well; (ii) in the next order the contributions to ?(2)(n) associated with the coe cients Nf CF CA and C2 ACF are generated, while the terms with the coe cients C3 F ; Nf C2 F ; C2 F CA are missed.... ..."

### Table 6.1. Performance comparisons. These data have been obtained on ST 0:25 2.5V, using an input width of 12 bits and performing 12 CORDIC iterations. In this way we have been able to achieve the same numerical accuracy as in the paper [6.18].

### Table 2. 22 dimensional feature vector describing an attribute source index description weight source index description weight 1 type of values (1 if has some numerical only values, 0 otherwise) 0.025 13 number of children attributes (nodes) all the way to leaf nodes

2002

"... In PAGE 4: ... The values of the feature vectors that are calculated in step 1.1 are described in detail in Table2 . The last six values from these vectors are calculated using the learning module of the XMapper.... ..."

Cited by 4

### Table 1: The submodels in numerical experiments

2006

"... In PAGE 14: ...We show the considered model and its submodels in Table1 , where {1, 2} is abbrevi- ated as 12. For example in the 5-way case we span M5 = {12, 23, 34, 45, 15} by M5 \ {15} and M5 \ {23} as illustrated in Figure 3.... ..."

Cited by 1