### Table 3: Slopes of the log-log plots at each quantile.

### Table 1: Data on log-log correlations between number of solutions and cost with n = 100, m=n varied and backbone size xed at di erent values.

2000

"... In PAGE 9: ...olutions against cost, where m=n is 4.29 and backbone size is 0.1n. A linear least squares regression (lsr) t is superimposed. Table1 gives summary data on the log-log scatter plot for di erent backbone sizes through the transition : the gradient and intercept of lsr ts, the product-moment correlation r and the rank correlation. The number of solutions is strongly and negatively related to the cost for smaller back- bone sizes through the transition and the strength of the relationship is fairly constant as m=n is varied.... ..."

Cited by 31

### Table 1: Data on log-log correlations between number of solutions and cost with n = 100, m=n varied and backbone size xed at di erent values.

2000

"... In PAGE 9: ...olutions against cost, where m=n is 4.29 and backbone size is 0.1n. A linear least squares regression (lsr) t is superimposed. Table1 gives summary data on the log-log scatter plot for di erent backbone sizes through the transition : the gradient and intercept of lsr ts, the product-moment correlation r and the rank correlation. The number of solutions is strongly and negatively related to the cost for smaller back- bone sizes through the transition and the strength of the relationship is fairly constant as m=n is varied.... ..."

Cited by 31

### TABLE II. Observed Equations for the Means and Standard Deviations in the Distributions of Energies of Random Threadings, Which are Estimated from Linear Fitting of the Log-log Plots of Energy Versus Sequence Length

1999

Cited by 2

### TABLE 3. FRACTAL DIMENSIONS OF ANTARCTIC COASTS (LOCATIONS ARE SHOWN IN FIGURE 2). R IS THE CORRELATION COEFFICIENT FOR THE LINEAR REGRESSION EQUATION FITTED ON THE LOG-LOG RICHARDSON PLOT

### Table 3 A ne scaling step characteristics for a problem with m = 6, n = 12, jBj = 4, in which A is rank de cient. k k = k k1, and the horizontal line represents the normal point of termination. Small log log log log

1999

"... In PAGE 25: ... In this case, we can replace 1=2 by in estimates of Section 5 such as (93), (95), and (98). Table3 illustrates another case in which jBj = 4, with the added complication that A is rank de cient. (We forced rank de ciency by setting A1j = 0 and A2j = 0 for j = 1; 2; ; n ? 1, so that the rst and second rows each contain a single nonzero in their last column.... ..."

Cited by 18

### Table 4 A ne scaling step characteristics for a problem with m = 6, n = 12, jBj = 8. k k = k k1, and the horizontal line represents the normal point of termination. Small log log log log

1999

"... In PAGE 25: ... The computational behavior is qualitatively the same as in Tables 1 and 2. Table4 illustrates a problem for which jBj = 8. Here, the coe cient matrices retain full numerical rank at all iterates, and the behavior is similar to that reported in Table 1.... ..."

Cited by 18

### Table 2 A ne scaling step characteristics for a problem with m = 6, n = 12, jBj = 4. k k = k k1, and the horizontal line represents the normal point of termination. Small log log log log

1999

"... In PAGE 25: ... This step length approaches 1 until the normal point of termination is reached, after which the errors in c xa and rb make further progress impossible. Table2 shows the interesting case in which we choose jBj = 4, so that the co- e cient matrix in (16a) has four singular values of magnitude ( ?1) and two of magnitude ( ). The second column shows that Algorithm modchol correctly iden- ti es the numerical rank during the last few iterations and that the interior-point algorithm continues to generate useful steps and to make good progress even after modchol encounters small pivots.... ..."

Cited by 18

### Table 1 A ne scaling step characteristics for a problem with m = 6, n = 12, jBj = 6. k k = k k1, and the horizontal line represents the normal point of termination. Small log log log log

1999

"... In PAGE 24: ... A horizontal line in each table indicates the iterate at which termination occurs according to the criterion (99). In Table1 we chose jBj = m = 6, making the linear program nondegenerate and the primal-dual solution unique. It is clear that c a and c sa satisfy the estimates (88) and (90), respectively, even when the algorithm is continues past the point of normal termination.... In PAGE 25: ... The second column shows that Algorithm modchol correctly iden- ti es the numerical rank during the last few iterations and that the interior-point algorithm continues to generate useful steps and to make good progress even after modchol encounters small pivots. Apart from this feature, the behavior is the same as in Table1 , with errors in c xa causing the interior-point algorithm to behave poorly when it is permitted to run past its normal point of termination. We noted that for all iterations, the \small quot; pivots were at the bottom right corner of the Cholesky matrix, so that (28) rather than the general estimate (27) applies to the perturbation matrix E.... In PAGE 25: ... Table 4 illustrates a problem for which jBj = 8. Here, the coe cient matrices retain full numerical rank at all iterates, and the behavior is similar to that reported in Table1 . One point of di erence is that the errors in c xa , which start to increase after iteration 19, do not have an immediate e ect on the residual rb.... ..."

Cited by 18

### Table 1. Comparison of PageRank and PAR.

"... In PAGE 12: ...depend on c (see Table1 ). In Figure 7 we present the log-log plots for PAR and PageRank.... ..."

Cited by 1