### Table 1. Test results of new limited memory method (L-BFGS-B) using primal method for

1995

"... In PAGE 19: ... This occurred only in some cases when the limited memory method was quite near the solution but was unable to meet the stopping criterion. In Table1 nact denotes the number of active bounds at the solution;; if this number is zero it does not mean that bounds were not encountered during the solution process.... In PAGE 23: ... However, a few observations on the two methods can be made. The results in Table1 indicate that the limited memory method usually requires more function evaluations than the SR1 option of Lancelot. (The BFGS option of Lancelot is clearly inferior to the SR1 option).... ..."

Cited by 88

### Table 3. Results of new limited memory method using three methods for subspace minimization

1995

"... In PAGE 23: ...uite similar due to use of the form described at the end of x5.3. Our computational experience suggests to us that the conjugate gradient method for subspace minimization is the least e ective approach;; it tends to take more time and function evaluations. Even though Table3 appears to indicate that the cg option results in fewer failures, tests with di erentvalues of m resulted, overall, in three more failures for the cg method than for the primal method. The limited memory method is sometimes unable to locate the solution accurately, and this can result in an excessive number of function evaluations (F1) or failure to make further progress (F2).... ..."

Cited by 88

### Table 2. Results of new limited memory method, using the primal method for subspace

1995

Cited by 88

### Table 9: NACA 0012 ow convergence results for old and new -limits. Grid 192 32 cells. 6 orders of magnitude drop in residual.

"... In PAGE 31: ... For the old limit, several di erent values of were used. The results are given in Table9 . The old and new limits perform similarly except for large values of for which a noticeable drop in convergence rate is typically observed.... ..."

### Table 9: NACA 0012 ow convergence results for old and new -limits. Grid 192 32 cells. 6 orders of magnitude drop in residual.

in A Robust Multigrid Algorithm for the Euler Equations with Local Preconditioning and Semi-coarsening

"... In PAGE 17: ... For the old limit, several di erent values of were used. The results are given in Table9 . The old and new limits perform similarly except for large values of for which a noticeable drop in convergence rate is typically observed.... ..."

### Table 5 Best multipliers a with regard to M24 new (limited search). m a M8 new M16 new M24 new

### Table 2. Results of new limited memory method, using the primal method for subspace minimization, for various values of the memory parameter m.

1995

Cited by 88

### Table 2 Example 9 Shu-Osher redone: We repeat Example 4, this time using a new limiter

1997

"... In PAGE 18: ...s the rectangle 0 x 1; 0 y 2. The initial data are chosen to be zero (to avoid over ow we set q1 = q2 = 10?12). We use in ow boundary conditions. In Table2 we showed that our component-wise convex ENO scheme (using 4th order Runge-Kutta) works well with no loss of accuracy. It was reported in [10] that dimensional spitting caused a loss of accuracy for this di cult problem.... ..."