### Table 5: Working values for the history and the update frequency parameters for strongly non-linear case Dimension History H Update frequency U 2 1400 1400 4 1800 1800 8 2000 2000

### Table 5.3: Major operating or planned superlaser facilities. Interactions of superlasers with matter are qualitatively very different from those of ordinary lasers because they have sufficient power (i.e., petawatt level) to induce strong relativistic, multi-photon, nonlinear, and direct nuclear (e.g., fission or fusion) effects.

2008

"... In PAGE 39: ...6 tritons, and hence, an excess of 0.6 triton per fusion reaction for a total energy release of about 25 MeV (see Table5 ). As is shown in this table, fission can also yield a net 0.... ..."

### Table 2 con rms the quality of our preconditioner even for strong in ucences of the nonlinearity. In the table we show results of computations for the shielding problem (cf. Section 6). We depict the number of QMR steps needed to reach a relative accuracy of 10 6. Even when 0 reaches large values, i.e. for jBj 1:5 (cf. Figure 2), we observe fairly good convergence properties of the QMR iteration. Computations were done on two di erent meshes and for various strength of the source current, i.e. for di erent induction in the solution, which is depicted in the second column. The third column in the table shows the iterative solution of the linear problem, whereas the subsequent columns display the Newton iteration and the number of QMR steps for the solution of the linearized problems.

2006

"... In PAGE 9: ... Table2 : QMR steps for the solution of the linearized problems in the Newton iteration. 5.... ..."

Cited by 1

### Table 7: Real and Predicted Runtimes of EX19 with strong scaling.

2002

"... In PAGE 11: ... This application is built on top of PETSc and comes from TOPS [15] and uses a nonlinear solver in a 2D driven cavity code with a velocity-vorticity formulation and a finite difference discretization on a structured grid. Table7 shows the results of these predictions for the same four machines using strong scaling. These predictions had an average 7% error (18% maximum) showing we can predict reasonably well on more complicated codes.... ..."

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### Table 2: Non-linear Data sets with f(x)=x

"... In PAGE 17: ... In these data sets the true R 2 was chosen to be larger than in the linear data sets in order to have a comparison in this range. But the multiple regression method was given the strong advantage of having the correct nonlinear function (see Table2 ), so only the coe cients and the constant term of the three non-linear components of the regression had to be estimated. With this considerable advantage the linear method is surely an optimal or nearly optimal... ..."

### Table 4: Elementary School Non-Linear Production Function

in Enhancing our Understanding of the Complexities of Education: "Knowledge Extraction from Data" using

### Table 2 Nonlinear models.

1998

"... In PAGE 16: ... Much of the emphasis will be on the choice of bandwidth and the new aspects brought in by using local polynomial approximation. A power experiment on a wide class of nonlinear models listed in Table2 has been conducted in Section 6.3.... In PAGE 18: ...Table2 , however, where M1(x) is approximately quadratic (see Figure 1), as can be expected the best result is achieved with T = 2 and h = 1. For the ^ L(V1)-tests the size tends to be too low.... In PAGE 18: ... If no corrections are made for this e ect, it will lead to conservative tests. Figure 5 shows the power of the ^ L(V )-tests for model la) of Table2 , and we see the same general trend as for the ^ L(M)-tests; the optimal h increases with T and the derivative. Here ^ L1(V1) also has some power for h = 1 because the variance is constant, not only linear, under the null hypothesis.... In PAGE 18: ... Here ^ L1(V1) also has some power for h = 1 because the variance is constant, not only linear, under the null hypothesis. ^ L0(V1) is much more robust than ^ L0(M1), and this is the case for the other models listed in Table2 as well. 6.... In PAGE 18: ... In particular when we have a nonlinear model, we do of course not want h = 1 to be chosen when T = 0 or T = 1, but with a small autocorrelation, this may well happen for T = 0. In fact h = 1 was chosen in 136 of 500 realizations of model lc) of Table2 which is clearly nonlinear (cf. Figure 1).... In PAGE 19: ... 6.3 A power experiment for a wide set of models We have performed a power experiment for the models listed in Table2 , where t N(0; 0:62) in model ld) - lf), t N(0; 0:72) in lg) - lj) and t N(0; 1) in the other models. Models la) - lj), aa) - ag) and Aa) - Ag) are discussed in Luukkonen et al.... In PAGE 36: ...Figure 1-2: Plots of ^ M1(x) (Figure 1) and ^ V1(e) (Figure 2) for the models listed in Table2 with n = 100 000. The kernel estimator with bandwidth h = 0:2 is used and each plot consists of two realizations.... In PAGE 36: ... The possible values for h is given at the vertical axes. Figure 7: The gure is based on 500 realizations of the models in Table2 . It shows the power of ^ LT (M1) with h cross-validated and n = 100, 250 and 204 for models la) - li), aa) - ag) and Aa) - Ag), respectively.... In PAGE 36: ...ower achieved in Hjellvik and Tj stheim (1995). The nominal size is 0.05. Figure 8: The gure is based on 500 realizations of the models in Table2 and shows the power of ^ LT (V1) with h cross-validated and n = 100, 250 and 204 for models la), aa) - ag) and Aa) - Ag), respectively.... In PAGE 37: ....05 for the standard normal distribution has been used. The model is Xt = t, the bandwidth is h = n?1=9 and the number of realizations are 500. Table2 : Various nonlinear models. Models la) - lj), aa) - ag) and Aa) - Ag) are discussed in Luukkonen et al.... ..."

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### Table 1: Nonlinear materials

2000

"... In PAGE 12: ... The soft material is a large deformation (Neo-Hookean) hyperelastic material with a mixed formulation [26]. Table1 shows a summary of the constitution of our two material types.... ..."

Cited by 3

### Table 4: Nonlinear Adjustment

2000

Cited by 2