### 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 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 2 Computational results for the test problems. A positive value in the last column means that the adaptive algorithm is faster. 5. Conclusion For interior point methods, with or without predictor-corrector strategies, we have presented an adaptive automated procedure for determining whether to use a direct or iterative solver, whether to reinitialize or update the precondi- tioner, and how many updates to apply, and demonstrated that it can enhance performance of interior point algorithms on large sparse problems.

1999

"... In PAGE 17: ... It is vitally important that the algorithm can make this decision automatically. Table2 shows the computational results on the three problem sets, com- paring the number of values needed by the interior point method, the relative duality gap in the nal answer, and the CPU time required by PCx and the adaptive algorithm. The last column is the di erence between the PCx and the adaptive times.... ..."

Cited by 10

### Table 4. 1 2 3

"... In PAGE 14: ... This is achieved by the standard predictor corrector procedure (see [35]) with two predictor{corrector steps. The approximation procedure is convergent, as is shown by the values of amp;i calculated for uf(t) = 1 + t as in Table4 and for uf(t) = et; uf(t) = e t as in Table 5. 5.... ..."

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

1953

Cited by 2

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

### 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 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 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