### Table 2. Edge weights for a4 -expansion edge weight for

"... In PAGE 5: ...edges are given in Table2 . These particular weights cor- respond to the energy function in equation 7.... ..."

### Table 4 Convergence of the special coarsening multigrid with di erent sizes of grid and jump. 5. Conclusions. From the energy-minimizing interpretation of the 1D interpolation, we have derived an analogous 2D interpolation which preserves constant and in a way minimizes the energy of decompositions of functions. The resulting multigrid methods has been shown theoretically pleasing and numerically e ective. Its purely algebraic implementation makes it particularly attractive to unstructured grids computations where geometric complications do not raise a problem. 10

1997

Cited by 8

### Table 4 Convergence of the special coarsening multigrid with di erent sizes of grid and jump. 5. Conclusions. From the energy-minimizing interpretation of the 1D interpolation, we have derived an analogous 2D interpolation which preserves constant and in a way minimizes the energy of decompositions of functions. The resulting multigrid methods has been shown theoretically pleasing and numerically e ective. Its purely algebraic implementation makes it particularly attractive to unstructured grids computations where geometric complications do not raise a problem. 10

1997

Cited by 8

### Table 8. Eigienvalues and measures of importance Percent Cumulative Canonical

"... In PAGE 7: ... Table8 gives these results. There are three nonzero eigenvalues, and they have been presented in the order of descending magnitude.... In PAGE 8: ... This is done by summing all the eigenvalues to get a measure of the total discriminating power, then, dividing this sum into each individual eigenvalue. (See Table8 .) Thus Function 1 contains 5 1.... In PAGE 8: ... If the residual discrimination is too small, then it is meaningless to derive any more functions, even if they exist mathematically. On the basis of Table8 , one should not form the conclusion that the first discriminant function will always have a large canonical correlation. Even though the first function is always the most powerful in a relative sense (as measure by the relative percentage), it may be only weakly related to the groups (as measure by the canonical correlations).... In PAGE 8: ...69 6 .oooo As shown in Table8 , the canonical correlations range from approximately .... ..."

### TABLE II. Results for some trinucleon bound state properties. Results, based on the two parameterizations (P) and (KB) of the P33 N interaction, are compared; the results for (P) are identical with those of Ref. [4] labelled H(1) there. The table lists the triton binding energies ET , binding energy corrections arising von non-nucleonic degrees of freedom in the de nition of Ref. [15], E2 being the binding energy correction of two-baryon nature; and E3 being the corresponding correction of three-baryon nature. The table also lists the wave function probabilities, i.e., PL for nucleonic components of total orbital angular momentum L = S; P; D and of particular orbital permutation symmetry, the probability P for components with a -isobar, and the probability P for components with a pion. The binding energies in the rst two columns result from exact Faddeev calculations, they are correct within 10 keV only, but the last digits in rows ET , E2 and E3 are believed to represent relative changes between the parameterizations correctly. The binding energy correction of rst order in QtBG(z)Q in the third column is derived in perturbation theory according to Eq. (4.2c).

### Table. 1. Particular fitness function for each stage

### TABLE II. Evaluation of Energy Functions

2003

Cited by 8

### Table I. Energy estimate functions.

2001

Cited by 1

### Table 1: Comparison of convergence results for the energy and other crucial quantities for

1998

"... In PAGE 3: ... However, for the present problem of a non-convex energy density, the results are rather sobering: In general, it can only be shown that a minimizing deformation u h 2A h satisn0ces En28u h n29 n14 Ch 1=2 ; n2810n29 where C denotes a generic constant that may depend on the topology of the quasiuniform triangulation T h and the domain n0a but not on the mesh-size h, see n5b8, 18, 17n5d, and n5b7n5d for a den0cnition of quasiuniformity.For a complete list of results for important quantities, see Table1 above. Moreover, it turns out that the quality of the approximation depends strongly... In PAGE 4: ... To this end, we present a new algorithm based on discontinuous n0cnite elements. It will be shown that this algorithm allows much improved convergence rate estimates for the energy, namely On28h 2 n29, and other quantities of interest as they are given in Table1 . In particular, the resolution of laminate microstructure on general meshes is much better than by the classical n28non-n29conforming discussed above.... In PAGE 7: ... The earlier case cancels out the contribution from the n28scaled, squaredn29 L 2 -norm of the deformation on the interior n0cnite elements and gives rise to an energy functional that is rotationally invariant, whereas the latter case is not rotationally invariant anymore, but allows for better approximation of the volume fractions. Again, we stress the fact that these convergence results are much better than those derived for the conforming n28using n28bi-, tri-n29linear ansatz functions, see n5b18n5dn29 or classical nonconforming n28using piecewise rotated n28bi-,trin29linear ansatz functions, see n5b18, 16n5dn29 n0cnite element methods, see also Table1 . This ren0dects the increased accuracy of the ansatz for non-aligned meshes: The misaligned triangulation does not lead to a dramatic pollution of the computed solution anymore.... ..."

Cited by 5