### TABLE III SOLUTIONS OF THE GRADIENT PROJECTION METHOD FOR THE NETWORK GIVEN IN FIGURE 7

### Table2:AccelerationErrorRates:HMM-MOSAIC/Gradient-MOSAICwith TwoTypesofInitialConditions.

"... In PAGE 15: ...Fiftyrepetitionsof20tri- alswereperformedforeachpairofswitchingperiodandinitialweight variance. Table2 showstheratioofthebullet5nalaccelerationerrorsofthetwolearning methods:theerrorofEMalgorithmdividedbytheerrorofgradient-based ethod.TheEMversionoftheMOSAICmodel(HMM-MOSAIC)provides morerobustestimationintwosenses.... ..."

### Table 4.c: Projection problems: variation of dimchol using = 0:01, = 0 and conjugate gradients

"... In PAGE 31: ...ables 4.a, 4.b and 4.c are constructed using the criteria of the previ- ous ones. Comparison of iterative linear methods is not meaningful here, because, as shown in Table4 .c, the direct method is much better than it- erative ones in this case.... In PAGE 31: ...ases where convergence was not achieved. The Average rows in Table 4.a were computed considering only the cases of convergence. In Table4 .b we computed the averages only for the two rst columns since these outperform clearly the last two.... In PAGE 31: ...ere computed considering only the cases of convergence. In Table 4.b we computed the averages only for the two rst columns since these outperform clearly the last two. Finally, in Table4 .c we computed the averages only for the last column, due to the same reasons as in Table 4.... In PAGE 31: ... Finally, in Table 4.c we computed the averages only for the last column, due to the same reasons as in Table4 .... In PAGE 32: ...50 2147, 5.42 Table4 .a: Projection problems: variation of ... In PAGE 33: ...27 2751, 7.55 { { Table4 .b: Projection problems: variation of using = 0:01, dimchol = 0 and conjugate gradients... ..."

### Table 4.b: Projection problems: variation of using = 0:01, dimchol = 0 and conjugate gradients

"... In PAGE 31: ...ables 4.a, 4.b and 4.c are constructed using the criteria of the previ- ous ones. Comparison of iterative linear methods is not meaningful here, because, as shown in Table4 .c, the direct method is much better than it- erative ones in this case.... In PAGE 31: ...ases where convergence was not achieved. The Average rows in Table 4.a were computed considering only the cases of convergence. In Table4 .b we computed the averages only for the two rst columns since these outperform clearly the last two.... In PAGE 31: ...ere computed considering only the cases of convergence. In Table 4.b we computed the averages only for the two rst columns since these outperform clearly the last two. Finally, in Table4 .c we computed the averages only for the last column, due to the same reasons as in Table 4.... In PAGE 31: ... Finally, in Table 4.c we computed the averages only for the last column, due to the same reasons as in Table4 .... In PAGE 32: ...50 2147, 5.42 Table4 .a: Projection problems: variation of ... In PAGE 34: ...5, 0.25 Table4 .c: Projection problems: variation of dimchol using = 0:01, = 0 and conjugate gradients 6 Conclusions Numerical experiments are, of course, quite dependent on the test problems used, so, the answers of the questions formulated at the beginning of the former section do not have an absolute value.... ..."

### Table 1 The projected conjugate gradient algorithm Initialize

"... In PAGE 13: ... The FETI-DPI algorithm is a classical conjugate gradient applied to the prob- lem (11). The algorithm is then similar with the one in Table1 , but no more projection is needed. One has to notice that at each iteration, this algorithm requires the solution of only one global coarse problem consisting in nding the displacement of corner dof, during matrix-vector product F ?v; as previously, the choice of the preconditioner is discussed in the next sec- tion.... In PAGE 20: ... With the equations (14), the overall problem to be solved is: 2 6 6 6 6 6 4 F F P Q G QT P T F L 0 GT 0 0 3 7 7 7 7 7 5 2 6 6 6 6 6 4 3 7 7 7 7 7 5 = 2 6 6 6 6 6 4 d QT P T d e 3 7 7 7 7 7 5 with L = QT P T F P Q To build the corresponding algorithm, the following ways are equivalent: using the FETI2 framework [32] with the interpretation of an additional coarse space correction with the regular matrix L, or, as it is done herein, condensing the new unknowns on the other ones to get: 2 6 4 F ? G GT 0 3 7 5 2 6 4 3 7 5 = 2 6 4 d? e 3 7 5 with F ? = F F P QL 1QT P T F and d? = d F P QL 1QT P T d, and apply the previous FETI-I algorithm to this new problem. the overall algorithm is the same as in Table1 ; the di erence in the implementation is the need for the additional coarse problem (with matrix L) within the matrix-vector product F ?p. The preconditioning step allows to apply the eventually singular (because incompressible) Dirichlet preconditioner to the residual: if s is a subdomain with all of its boundary subjected to a prescribed displacement v(s) = B(s)T W P T P s B(s)u(s), the Dirichlet problem to be solved on this subdomain is: K(s) Hii 2 6 4v(s) i p(s) 3 7 5 = 2 6 4 f K(s) ib C(s) b T 3 7 5 v(s) b If K(s) Hii is singular, its kernel is exactly a uniform pressure 0 p(s) 1 T T .... ..."

### Table 3-2: Gravity Gradient Acceleration Simulation Results Altitude Gravity Gradient Acc (m/s2)

"... In PAGE 11: ...List of Tables Table3 -1: Aerodynamic Force Acceleration Simulation Results.... In PAGE 11: ...able 3-1: Aerodynamic Force Acceleration Simulation Results....................................11 Table3 -2: Gravity Gradient Acceleration Simulation Results .... In PAGE 11: ...able 3-2: Gravity Gradient Acceleration Simulation Results ........................................13 Table3 -3: Results of Range Error Study Between Exact Ephemeris and Ephemeris Generated From Osculating Elements at Periapsis .... In PAGE 25: ...ass equal to 760 kg, reference area equal to 17.03 m2, and Cz equal to 2.0. The results of the simulation are shown in Table 3-1. Table3 -1: Aerodynamic Force Acceleration Simulation Results Altitude (km) Simulated Density (kg/km3) Aero Acceleration (m/s2) 170 0.005 2.... In PAGE 26: ...nstrument was assumed to be 0.44 meters in the R-direction and 0.38 meters in the Z- direction. The results of the gravity gradient acceleration are shown in Table3 -2 for... In PAGE 27: ...5*10-7 m/s2. As shown in Table3 -1, the maximum gravity gradient is less than 1 percent of the aerodynamic acceleration below 140 km. However, the gravity gradient component is approximately 22 percent of the 170 km acceleration estimate.... In PAGE 36: ... Available from MGS NAV Team] are shown in Table 3-3. Table3 -3: Results of Range Error Study Between Exact Ephemeris and Ephemeris Generated From Osculating Elements at Periapsis Time From Periapsis (sec) Approx. Areodetic Altitude (km) Range Error [Exact-Kepler] (km) 240 186.... ..."

### Table 2. cg-accelerated iteration methods

1998

"... In PAGE 26: ... Only the action of ^ A 1 and ^ C 1 to a known vector is required. Table2 shows the results of the numerical experiments. For each mesh from level 4 to level 8 it contains the numbers n and m of unknowns, the iteration numbers N and the averaged convergence factor =(ek=e0)1=k in comparison with (an upper bound of) the theoretical convergence factor th =[2ck=(1+c2k)]1=k in the A-norm, where c =(p 1)=(p + 1) (see, e.... ..."

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### Table 3: Accelerating gradient history of the single-cell reentrant cavity at 2 K.

2004

"... In PAGE 2: ... Sometimes, gas helium process- ing was performed with a best improvement from 37 to 43 MV/m (16%) in the accelerating gradient. A summary of RF test results is given in Table3 . With an accumulated surface removal of 18 a94 m by BCP1:1:2 for the welded single-cell cavity, an accelerating gradient of 27 MV/m was already reached during the second test at a Qa3 of a97a98a6a15a5a10a9a50a99 .... ..."