### Table 1 Comparison of the convergence rate for the fast Maxnet and the Maxnet Data set Fast Maxnet Maxnet ratio

"... In PAGE 4: ... 1. Comparison of the Convergence Rate If Maxi- mum is Uunique After both algorithms are applied, the results of uniform distributions are listed in Table1 . These re- sults include (1) the required iterations for conver- gence of both models, (2) their respective ratios.... In PAGE 5: ... The effects of mutual inhibitions decrease gradually. Furthermore, Table1 gives an- other indication that the convergent ratio (processor nodes / iterations) of the Maxnet decreases if the in- put data increases. So, the convergence rate is very slow if the input data are very numerous.... In PAGE 5: ... Comparison of Computational Steps The steps that must be performed, serially, at each iteration are 4 and 2 for the fast Maxnet and the Maxnet, respectively. The total computational steps of uniform distributions are listed in the parentheses of Table1 . The slow convergence rate of the Maxnet when the input data are very numerous is very conspicuous.... ..."

### Table 1: GA parameters that lead to fast convergence

"... In PAGE 5: ... maximum tness vs. number iterations on problem 7 in Table1 for both. CIGAR replaces fteen percent (15%) of the population with individuals from the case base every four (4) generations.... ..."

### Table 1: Convergence of the Algorithm

1992

"... In PAGE 19: ...1 2 3 4 m2 0:50000 0:83333 0:75000 0:75873 n 5 6 7 8 m2 0:75133 0:75334 0:75225 0:75681 Table1 : Convergence of the Algorithm The explicit form of the stationary density is p(x) = Cr?1=2e 1(r+x1) cos ( =2) ; x = (x1; x2) = (r cos ; r sin ); (30) where C = ?1=2 (2j 1j)3=2. (Greenberg [10] pointed out that Harrison apos;s [11] original cal- culation of C was in error by a factor of 2.... In PAGE 19: ... It was rigorously proved in [11] that the one-dimensional marginal distribution of x1 is indeed of exponential form. Table1 shows that if we require one percent accuracy, which is usually good enough in queueing network applications, the convergence is very fast, even for this very singular density. It appears that the accuracy of m2 does not increase as n increases.... ..."

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### Table 2 Comparison of the fast Maxnet and the Maxnet under non-unique maxima Data set Fast Maxnet Maxnet ratio

"... In PAGE 5: ...maller than 0.1. However the convergence rate of the Maxnet is still very slow. The results of nonuni- form distributions are listed in Table2 . In Table 2, Dmax(1,8192;2) of the Maxnet is null because the pro- gram could not finish within two days.... ..."

### Table 6.1: Algorithm start. and the optimal levels qi;S has been determined for every time interval, one problem (6.2) is solved to obtain a solution satisfying all constraints. Since we have to solve problem (6.2) many times with an iterative algorithm, the need for good starting values is obvious. To ensure convergence in practice and shorten the total evaluation time a starting value algorithm has to be fast and give starting values xstart i

### Table 1. Distribution of journal titles and requests satisfied by regions

"... In PAGE 11: ... 3 For convenience, data containing the first set will be labeled 2000 and the second set 2001 . 4 The discrepancy between total requests fulfilled as given in Table1 (92,574 ) and that of 91,314 is due to the lack of journal data for 1260 article requests. 5 We used the subject categories given in SCI Journal Citation Reports (2001) to classify journal titles under each subject category.... In PAGE 13: ... The total number of journal titles (5521) were divided into three equal regions on the basis of total requests that journal titles in each region satisfied (in our case, one-third of all requests for each region). Table1 below gives the number of journal titles and approximate percentages of transactions satisfied. As we indicated earlier, 168 core journals satisfied one-third of all requests whereas 667 titles (499 plus 168) satisfied two-thirds of all requests.... ..."

### Table 1 Convergence Results for Variant Algorithm. Numbers of iter- ations needed to satisfy (61) are given in the column labeled DD. The numbers in parentheses are the number of iterations required to satisfy the convergence criterion described in Section 5.

2007

"... In PAGE 15: ... (61) This is more stringent than necessary for purposes of com- puting an approximation to the solution of the partial differ- ential equation, but it allows us to illustrate the behavior of the solver as an iterative method for solving linear systems of equations. Table1 summarizes this computation. The columns la- beled DD indicate the number of domain decomposition Fig.... ..."

### Table 1: Iteration counts for iterative solutions of FIT2P. Algo- rithm switched phase at step 17.

"... In PAGE 22: ... The results for FIT2P are tabulated in Table 1. Table1 : Iteration counts for iterative solutions of FIT2P. Algo- rithm switched phase at step 17.... In PAGE 23: ...Indeed, as shown in Table1 , the number of PCG iterations taken to solve the normal equations generally increases as the IPM converges to a solution. On the other hand, when the two-phase algorithm switches to the RAE system (which occurs at the 17th IPM step), the number of SQMR iterations taken to solve the preconditioned RAE system generally decreases as the IPM solution converges.... ..."

### Table 10: does not satisfy (H2)

1997

"... In PAGE 23: ... The other conditions in (H2) and (H1) hold, and we can take d = =2. Despite the fact that does not satisfy conditions (H2), we still have the convergence of the Ka canov iteration method, and the a posteriori error estimate is e cient (see Table10 and Figure 2).... ..."

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