### Table 7 Average number of CG iterations on the ne grid for the oscillatory coe cient problem. = 0:1; 0:01. Example 5: We show by a one-dimensional Helmholtz equation that the energy minimization principle is not restricted to positive de nite second order elliptic PDEs. The model equation is u + u = 1; (24)where is a positive constant. This operator is inde nite. We use multigrid to solve the linear system Ah. For this problem, we obtained H i from solving the local PDEs (7), not from the minimization problem (12), since constant functions are not in the 16

1998

Cited by 28

### Table 1. Query-update cost tradeo s for selected one-dimensional techniques

2001

"... In PAGE 8: ... Since we focus on techniques that do not introduce space overhead, PS is the approach with the minimal query cost. Table1 summarizes the query and update costs for selected one-dimensional techniques.... ..."

Cited by 13

### Table 8.3: System level optimization using one-dimensional optimization

### Table 1. Maximum Simulated Likelihood Estimation Results for One Dimensional Integration

in Abstract Quasi-Random Maximum Simulated Likelihood Estimation of the Mixed Multinomial Logit Model

"... In PAGE 20: ... The important point to note, however, is that these are minor aberrations to the more stable general trend of reduced errors with higher draws. The results for one-dimensional integration ( Table1 ) indicate that with as few as 50 Halton draws, the error measures from the QMC method are smaller than from 1000 draws of the PMC method; those from 75 Halton draws are much smaller than from 2000 pseudo-random draws. Besides, the times to convergence for the QMC method are considerably lesser than for the PMC method.... In PAGE 31: ... Table1 . Maximum Simulated Likelihood Estimation Results for One Dimensional Integration Table 2.... ..."

### Table 11. Parameters used in MOC3D simulation of transport in a one-dimensional, steady-state flow system

"... In PAGE 9: ... Numerical (MOC3D) and analytical solutions at three different locations for solute transport in a one-dimensional, steady flow field. Parameter values for this base case are listed in Table11 .... In PAGE 9: ...0 cm, Dxx = 0.1 cm2/s, and other parameters as defined in Table11 ) .... In PAGE 10: ...01 s-1. All other parameters as defined in Table11 .... In PAGE 90: ...APPENDIX C: ANNOTATED EXAMPLE INPUT DATA SET FOR SAMPLE PROBLEM This example input data set is the one used to generate the solution for the base case in the one-dimensional steady-state flow problem. Parameter values are indicated in Table11 and selected results are shown in fig.... ..."

### Table 6. Parameters used in implicit MOC3D simulation of solute transport in a one-dimensional, steady-state flow system

### Table 4: Results for routing on one-dimensional arrays. Ratetriv and Rateopt indicate the number of MB / s that are transferred over the bisection. We see that as soon as the bisection gets critical, for P 9, the optimal strategy gets more out-of the bisection than the trivial one. The difference corresponds quite well to the theoretical possibilities. Further improvements can be achieved by minimizing the length of the cycles inside the permutations (a permutation that consists of P=2 exchanges is considerably faster than one cycle of length P). As this only has a positive effect for routing on one-dimensional arrays, we did not optimize for this criterion.

1997

Cited by 4

### Table 1: Left: The trivial decomposition of an all-to-all routing on a one-dimensional processor array of length eight into eight permutations. Right: An optimal decomposition of an all-to-all routing on a one-dimensional processor array of length eight into eight permutations.

1997

"... In PAGE 6: ... Right: An optimal decomposition of an all-to-all routing on a one-dimensional processor array of length eight into eight permutations. The trivial schedule is represented in Table1 on the left. The entries in the table indicate the phase in which a packet is routed from the PU indicated in the first row, to the PU indicated in the first column.... In PAGE 6: ...he first column. For example, we see that PU4 routes in Phase 6 to PU2. That each PU sends and receives only one packet at a time, implies that all numbers should occur only once in every row and column, respectively. From Table1 we can immediately see the unbalanced character of the trivial strategy: in the indicated top-right quarter, there are four 4-s, and no 0-s. Without knowing the structure, this tells us that during Phase 4, four packets have to be routed over the bisection of the network, the connection from PU3 to PU4, and no packet during Phase 0.... In PAGE 6: ... Without knowing the structure, this tells us that during Phase 4, four packets have to be routed over the bisection of the network, the connection from PU3 to PU4, and no packet during Phase 0. Now consider our alternative in Table1 on the right. Here all numbers 0; 1; : : :; 7 occur exactly twice in the 16 positions of the upper-right corner, indicating that in every Phase exactly two packets have to go over the bisection.... In PAGE 6: ... Because we are considering permutations, the rightwards connections are as heavily loaded as the leftwards connections. What does this mean? Let us consider the cost of bata routing with the decomposition on the right side of Table1 . In each of the eight permutations a PU sends and receives at most one packet.... ..."

Cited by 4

### Table 2: The one-dimensional categorisation of Stacheldraht

"... In PAGE 145: ... Often it is regarded as only attacking the host computer, the computer it is residing on, but this definition is far from being generally accepted. The new proposed definition, which can be seen in Table2 , is meant to be rather general. There are several categories which are marked with wildcard that might be used to narrow the definition a bit.... In PAGE 148: ...Worm 133 Table2 : The redefined term virus Category Alternative 0/1/wildcard Type atomic wildcard Type combined wildcard Violates confidentiality wildcard Violates integrity;parasitic 1 Violates integrity;non-parasitic wildcard Violates availability wildcard Dur. of effect temporary wildcard Dur.... ..."

### Table 3: The one-dimensional categorisation of TFN

"... In PAGE 145: ... The things setting them apart are that worms are defined as being self-standing (not being parasitic) and often also as replicating over network connections. The new, proposed definition is shown in Table3 and as for the new definition of virus it is rather general and hence might also be narrowed down a bit. First of all, the Affects; integrity;non-parasitic alternative may really be needed,... In PAGE 149: ...1 INTRODUCTION Table3 : The redefined term worm Category Alternative 0/1/wildcard Type atomic wildcard Type combined wildcard Violates confidentiality wildcard Violates integrity;parasitic 0 Violates integrity;non-parasitic wildcard Violates availability wildcard Dur. of effect temporary wildcard Dur.... ..."