### Table 3. Comparison of predictor-corrector cases ~~ ~

in Preface

1971

"... In PAGE 35: ...ig. 5. Tropospheric doppler effect This quantity gives the percentage error of the tropo- spheric doppler effect induced by mapping with the nomi- nal profile, scaled by the zenith range effects, instead of by mapping with the correct profile. Table3 lists the results of computing 8i at several ele- vation angles for the 20 profiles given in Table 1. As was the case for Table 2, if the calculations were performed using the unrefracted elevation angles yl, instead of yo, the changes in the values would only be of the second order.... In PAGE 35: ... As was the case for Table 2, if the calculations were performed using the unrefracted elevation angles yl, instead of yo, the changes in the values would only be of the second order. Once more, some idea of the error bound on 8j may be found by adding the magnitudes of the largest doppler mapping errors from each of the six groups of profiles in Table3 , for each elevation angle. If the somewhat un- realistic profiles 1 and 2 are ignored, this tentative error bound is 2.... In PAGE 36: ...Table3 . Doppler mapping error for various profiles and elevation angles Profile group Profile number s;, % Observed surface elevation angle, dag I I ~ 1 I 16.... In PAGE 41: ...ig. 2. Partials of Surveyor 111 two-way doppler with respect to N, R, LO, and LA 240 280 270 to a new minimum. s The solutions are presented in Table3 , and the response of the spin-axis distance solu- tions of each DSS to the assigned N values is graphed in Fig. 5.... In PAGE 41: ...ig. 3. Partials of Surveyor 111 two-way doppler with respect to Aa/o, Ae, AL f Ar, and Ap this time): the first series of fits solved for N, ra, h (DSS refractivity scalers, distance off the spin axis, and longi- tudes, respectively); the second series of reductions solved for N, rs, and A, but N was constrained by an a priori u equal to 2% of the nominal value of N; and, finally, the third series solved for N solely. Table3 . Solution parameter sensitivities to N 0 0 0 5206.... In PAGE 67: ...160*00 With T = K sec and R, = 1 a, Table 2 provides all the information necessary to determine the primed filter. A specific example is shown in Table3 which refers to filters associated with a 10-ps bit time and a 50-a generator. V.... In PAGE 68: ...Table3 . Network elements for T = 10 ps, R, = 50s2 ***UNIlS*** ~ICROSECON0~RE6AWER1t,OHW sM ICROHENRYn HICROFllRlD 1: I .... In PAGE 126: ... C. Comparison of Predictor-Corrector Cases Table3 contains a comparison of several predictor- corrector cases. This table has the same format as Table 1.... ..."

### Table 1: The e ect of the use of trust region technique in ACCPM.

"... In PAGE 13: ...2. We compare in Table1 two di erent variants of ACCPM: the one without the trust region technique (bounds in this case are set to l = ?104 and h = +104, respectively), and the one applying the trust region technique. The initial trust region is a box of size 102 around the initial estimate of u.... In PAGE 13: ... In both cases the subproblems are solved to optimality, which means that exact subgradients are used. In Table1 we report the number of outer iterations (subproblem calls), the number of inner iterations, i.e.... In PAGE 19: ...Table1 0: E ciency of the warm start routine. Problem Exact subgradients quot;-subgradients AC OPT AC OPT MARKAL 4 13 4 11 MACHINES 1 5 1 3 ENERGY-S 3 10 3 7 ENERGY-L1 6 15 6 11 ENERGY-L2 4 16 4 10 The analysis of the results collected in Table 10 con rm that when the sequence of linear programs with varying objective functions is solved, the reoptimizations with the infeasible primal-dual method can be done quite e ciently.... ..."

### Table 1: The e#0Bect of the use of trust region technique in ACCPM.

1997

"... In PAGE 13: ...2. We compare in Table1 two di#0Berentvariants of ACCPM: the one without the trust region technique #28bounds in this case are set to l = ,10 4 and h = +10 4 , respectively#29, and the one applying the trust region technique. Initial trust region is a box of size 10 2 around the initial estimate of u.... In PAGE 13: ... In both cases the subproblems are always solved to optimality, which means that exact subgradients are used. In Table1 we report the number of outer iterations #28subproblem calls#29, the number of inner iterations, i.e.... In PAGE 19: ...Table1 0: E#0Eciency of the warm start routine. Problem Exact subgradients quot;-subgradients AC OPT AC OPT MARKAL 4 13 4 11 MACHINES 1 5 1 3 ENERGY-S 3 10 3 7 ENERGY-L1 6 15 6 11 ENERGY-L2 4 16 4 10 6 Conclusions In this paper we discussed several enhancements of the analytic center cutting plane scheme for block angular linear programs.... ..."

### Table 3 (a) Number of iterations to reduce gap by 1012 averaged over 100 randomly generated problems. Mehrotra predictor-corrector rule; starting infeasible; S: short step failure (not included in average).

1995

"... In PAGE 20: ... More aggressive choices of gave a signi cantly reduced number of iterations (without loss of feasibility) for the XZ+ZX method, but led to many failures for the XZ and NT algorithms. In Table3 , we show results for the XZ+ZX method when the problem size n is varied, using the PC rule and two choices of . We see an iteration count which is essentially constant as n increases, with occasional failures (with steps too short) for =0:999.... ..."

Cited by 424

### Table 1 Results of Standard/Tensor with line search for Pb1 and Pb2, and with trust region for Pb3 Standard Tensor

"... In PAGE 2: ... The comparison is fair as both the tensor and standard programs generate the same sequence of iterates and consequently perform the same number of Jacobian evaluations and QR factorizations, since there is no algorithmic di erences between the parallel tensor code and TENSOLVE. Table1 is a representative of the times, speedups, and e ciencies of the standard and tensor methods, for test problems 1, 2, and 3, respectively. We ran cases where the size of TENSOLVE does not t into one node to study the behavior of the e ciency for p = 32.... In PAGE 2: ... We ran cases where the size of TENSOLVE does not t into one node to study the behavior of the e ciency for p = 32. Such values are preceded by the gt; sign in Table1 . The following are the key observations... ..."

### Table 1 Multistep predictor corrector time integration procedure Algorithm A : This algorithm allows for a single time step update in the multi- step predictor corrector time integration procedure used to integrate the system of Eqs. (5.4)

### Table 1. Percent identity of the results produced by the various algorithms with the reference alignments given by BAliBASE (according to the column score of trusted regions). The alignment count is given in parentheses after each group in the top row

2003

"... In PAGE 4: ... Notredame (personal communication). Table1 summarizes the main results. For each group of alignments from the BAliBASE data set, the average percentage identity with the reference alignments is given, taking into account structural columns as annotated in BAliBASE.... In PAGE 4: ... For each group of alignments from the BAliBASE data set, the average percentage identity with the reference alignments is given, taking into account structural columns as annotated in BAliBASE. A basic version of our program denoted by Mixed T = 0 in Table1 uses the entire set of fragments returned by DIALIGN as constraints for the divide-and- conquer alignment. In addition, we performed runs where the cutoff value T was set to higher values, such that only fragments with overlap weights above T were used.... In PAGE 4: ...l. (1994) and T-COFFEE Notredame et al. (2000). As can be seen from Table1 , the strengths of DCA and DIALIGN differ substantially. The mixed approach shows characteristics of both strategies, refining the segment-based local alignment computed by DIALIGN with the divide-and-conquer hyperspace alignment strag- egy(DCA).... In PAGE 5: ...nto the global alignment (i.e. it scores better than any of the underlying strategies alone). Concerning the influence of the cutoff parameter on the quality of the resulting alignment, it can be seen from Table1 that the best value for T depends on the characteristics of the input data. In the first three groups of BAliBASE where DCA is superior to DIALIGN, a high cutoff prevents spurious fragments from deteriorating the final alignment and increases the quality of the program output.... In PAGE 6: ... On the one side, the mixed method takes full advantage of the hyperspace alignment, while it reduces the computational time (and space) requirements necessary for this method (see Table 2). In most reference groups, the average results can reach a value close to the T-COFFEE algorithm (see Table1 ), and they are generally faster calculated. Single alignments within a group of the BAliBASE reference set are even outperforming results of the T-COFFEE algorithm (see Table 3).... ..."

### Table 7 Modi ed Hessians with trust region

1994

"... In PAGE 16: ... The measure of distance to feasibility (the {tube strategy), the nonmonotone updating of penalty parameter d, and the trust region strategy were essentially dormant during the solution process regardless of the iterates apos; proximity to the solution or to feasibility. In fact, the only evidence of our enhancements on the small number of CUTE test problems that we solved occurred when d was decreased slightly while solving the problem MANNE employing modi ed Hessians with a trust region strategy (see the third and fourth rows of Table7 ). It is noteworthy that the iterates that resulted from solving this problem with the penalty parameter arti cially held xed at d = 1 were identical to iterates that resulted for the adjusted d solution.... ..."

Cited by 27

### Table 1. Frame rates for a trust-region tracker and a mean-shift tracker, respectively.

"... In PAGE 5: ... The results we obtain are encour- aging, and they support our speculation that a trust-region based tracker should outperform a linesearch-based tracker. Some of the test results are shown in Figure 4, where the frame rates for each test are listed in Table1 . For the future work, we are now working on extending the trust-region tracker to handle scale and orientation changes, and to track multiple objects simultaneously.... ..."

### Table 1. Frame rates for a trust-region tracker and a mean-shift tracker, respectively.

"... In PAGE 5: ... The results we obtain are encour- aging, and they support our speculation that a trust-region based tracker should outperform a linesearch-based tracker. Some of the test results are shown in Figure 4, where the frame rates for each test are listed in Table1 . For the future work, we are now working on extending the trust-region tracker to handle scale and orientation changes, and to track multiple objects simultaneously.... ..."