### Table 2 lists the simulation results of tracking a composite trajectory (Figure 10). Again both Schemes A and B outperform Ishiguro et: al apos;s scheme and Scheme B is the best. In both simulation cases, Scheme C has comparable performance as Ishiguro et: al apos;s scheme. The tracking responses of Schemes A, B and Ishiguro et: al apos;s scheme are shown in Figures 10,11,12, respectively.

"... In PAGE 12: ...Table2 . Composite tracking errors during the second iteration( is optimized.... ..."

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### Table 4: Performance of different collaboration schemes in the discretized Booth problem domain. 10*5+2*rest significantly outperforms all other settings.

"... In PAGE 7: ...Table4 . The 10*5+2*rest method has a sig- nificantly better performance than all fixed settings.... ..."

### Table II shows the L1 norm of the errors. Though the results are eld dependent, the \quantitative picture quot; is favourable with the central di erencing schemes. Table III shows the time performance of the various schemes. All the schemes have time performances of order O(NX)2, where NX is the number of spatial cells. Figures 5.1-5.4 include a comparison between the numerical solution and the exact solution (shown by the solid line), e.g. [3], [20], at t = 0:1644. As expected, the overall resolution of the rst order schemes is outperformed by the second order schemes. We observe that our second order staggered schemes, STG, STG2, and STGU, and similarily, the second order upwind ULT1 scheme, smear the shock discontinuity over two cells. The contact discontinuity, however,

1990

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### Table 3: Performance of different collaboration schemes in the discretized Griewangk problem domain. 10*5+2*rest significantly outperforms all other settings, except for 8 collaborators.

### Table 3: Results for problem P4 and P5. The results suggest that all four versions of local search perform well but this is rather tentative. More computational experiments are necessary to get a clearer pic- ture. The questions of whether or not HVS schemes are capable of outperforming LS in certain situation, and the best values of the various parameters in LS are currently under investigation.

2000

"... In PAGE 13: ...3 Table 2: Results for problem P1, P2 and P3. In order to investigate the e ect of the di erent LS constraint selection schemes, Table3 gives the results for HDS and the four di erent choices for select-unsatis ed- constraint. The parameters for LS are identical with Table 2 except that Max moves = 50000 and Max tries = 4 for P5.... ..."

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### Table 1: Performance of different collaboration schemes in the discretized two-peak problem domain. 10*5+2*rest significantly outperforms all other settings.

"... In PAGE 5: ... This problem domain is illustrated in Figure 1. The results are summarized in Table1 . The results for our decreasingly lenient setting, 10*5+2*rest, are signif- icantly better than the ones for all other settings.... ..."

### Table 2: Performance of different collaboration schemes in the discretized Rosenbrock-like problem domain. 10*5+2*rest significantly outperforms all other settings.

### Table II: Noise statistics of the sets SA and SB. The figures in brackets are the average number of errors per word. The three algorithms, Levenshtein Distance (Algorithm_LD), the Generalized Levenshtein Distance (Algorithm_GLD) and our algorithm (Algorithm_OPT_PR), were tested with the sets of 1026 noisy words, SA and SB. The results obtained in terms of the recognition accuracy for the two sets are tabulated below in Tables IV. Note that our scheme far outperforms the traditional string correction algorithm (eg. 97.66 % instead of 94.93 % in SA). It also outperforms the GLD algorithm (eg. 96.49 % instead of 94.35 % in SB). The reader should observe that, as in all PR problems, it is much harder to increase the recognition accuracy at the higher end of the spectrum. The power of our strategy is obvious !!

### Table 2. Composite tracking errors during the second iteration( is optimized.) Scheme A Scheme B Scheme C Ishiguro apos;s Uncompensated

"... In PAGE 11: ...0045 8.5890 Table2 lists the simulation results of tracking a composite trajectory (Figure 10). Again both Schemes A and B outperform Ishiguro et: al apos;s scheme and Scheme B is the best.... ..."

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### Tables 3 and 4 illustrate the performances of various vector- ization schemes for the FBS phase. The last column of Table 3 shows the execution time of DS phase for all schemes. As seen in Tables 3 and 4, PRI outperforms GRI due to both the chain- ing and the substantial reduction in the number of redundant scalar additions achieved by the proposed re-ordering algorithm.

1995

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