### TABLE I. - ComrcrEms rN DIFFERENCE-DIFFERENTIAL EQUATIONS FOR CERTAIN PREDICTOR-CORRECTOR FORMUUS

### Table 2: Explicit Euler computations on the Intel Paragon : NX communication library CPU for 100 iterations of the predictor/corrector scheme Increasing problem size and overlapping (upper) and non-overlapping (lower) mesh partitions MESH Np CPU M op/s Loc Comm Glb Comm

1996

"... In PAGE 50: ...0 s 2697.0 s Table2 0: Implicit Euler computations on the ONERA M6 wing with mesh M2 Computations on a Dec 3000/700 workstation Total CPU times for steady state computations Solver CPU Matrix Inver Jacobi 3995.0 s 3399.... ..."

Cited by 4

### 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 6.1: Number of factorizations from Mehrotra apos;s predictor-corrector algo- rithm with di erent heuristic in equation (6.18). The alternatives are de ned by (6.11) and (6.20).

### Table 5.3 TRUSS Number of nonzero entries the predictor-corrector variant because the preconditioner is used for solving two lin- ear systems.

1953

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### Table 1. FEFLOW Model Inputs for the Hypothetical Simulation Cases

"... In PAGE 9: ... The so-called boundary constraint condition available in FEFLOW simulator is utilized to achieve the described mass boundary. Three hypothetical cases were simulated to verify the accuracy of the analytical solutions ( Table1 ). An iterative solution for steady flow and mass transport was obtained for case 1.... In PAGE 10: ...5 M Table 3. Numerical Specifications in FEFLOW Topic Quantity Mesh type 3-noded triangle elements (82,162 to 555,696) Finite element scheme no upwinding (best-accurate Galerkin-based formulation) Problem class combined flow and mass transport Time stepping scheme automatic time step control via predictor-corrector schemes (AB/TR time integration scheme) Mass transport equation convective form transport Iterative solver preconditioned conjugate gradient PCG Density coupling Boussinesq approximation Evaluation of element integral standard Gauss quadrature Velocity approximation improved consistent velocity approximation (by Frolkovic- Knabner) Comparison of the results from numerical simulation and those from the analytical solution Three hypothetical cases ( Table1 ) are utilized to verify the accuracy of the analytical solutions. Figure 3 depicts white streamlines in the mixing zone superimposed on shaded concentration fringes, which represent the density-driven seawater circulation in the coastal aquifer.... In PAGE 12: ... Figure 4 compares the 0.5Cs isochlors at steady state for the three cases in Table1 with the corresponding saltwater interfaces obtained from the analytical solutions. The accuracy of the analytical solution is somewhat limited by assumptions such as Dupuit-type flow and the... ..."

### 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 5.4 Type-II SDPs, Without Block LU Factorization The HKM method with PT P = Z, without the SVD, as discussed in x4.2. The method discussed in x5.1. We will call it the New method. The NT method in our experiments is not identical to the NT method in [26, 27, 29]. However, as we argued at the end of x4.4, we expect both variations to su er from similar numerical instability problems. For comparison, we also implemented the above four methods by solving the corresponding equation (2.2) with a backward stable dense linear equation solver, with proper re-scaling whenever necessary. In all cases, we set the initial guess to be X = Z = I and y = 0. We chose = 0:25 and = 0:98, and switched to the Mehrotra predictor-corrector versions as soon as2 krpk kAk kXkF +

1997

Cited by 5

### Table 2: Iterations of the predictor-corrector type method. Centering steps are indicated by `c apos; and -update steps by `p apos;. The values of the proximity and duality gap after each step are shown, as well as the update parameter at each -update.

2002

Cited by 1