### TABLE II WAVELET QUASI-INTERPOLANT PREFILTERS

1999

Cited by 37

### Table 1: Least-squares (LSQ) and quasi-interpolation (QI) errors.

"... In PAGE 3: ... For sl no initial surface is needed. The results of our experiments are reported in Table1 for a set of functions z = f(x; y), (x; y) 2 [ 1; 1]2, chosen to examine the behavior of the approximation under a variety of conditions: a smooth deformation with decay at infinity (Fig. 3a); a smooth deformation with oscillations (Fig.... ..."

### TABLE I COEFFICIENTS 1049110793 IN (27), (28), and (30) FOR THE PROPOSED QUASI-INTERPOLATION PREFILTERS.THE COEFFICIENTS OF THE DISCRETE FILTERS 98

### Table 2: Method of lines solution for transport equation.

"... In PAGE 10: ... The simulation is allowed to run for t from 0 to 2. The results displayed in Table2 are the maximum error at the final time evaluated on a fine evaluation mesh, along with an indication of the h-convergence rate of the method. We see that the use of a more accurate quasi-interpolant pays off and results in higher accuracy.... ..."

### Table 2 shows that for a larger (but xed) bandwidth the algorithm also stops converging. However, this happens at a later stage (around iteration 9 instead of iteration 5). In this case, a decrease in the reduction of the residual is just starting in the last few iterations. A phenomenon similar to this was described in [17] in the context of quasi-interpolation with Gaussian kernels, and referred to as approximate approximation by the authors. The fact that the `2 errors are on the order of machine pre- cision is no reason for concern, since the absolute value of the error is still on the order of 10?7, and the `2 errors are computed via 1=n P jerrorj2.

in Algorithms Defined by Nash Iteration: Some Implementations via Multilevel Collocation and Smoothing

"... In PAGE 16: ... Table2 : Newton iteration without smoothing. Constant (but larger) bandwidth.... ..."

### Table 3. E ect of reconstruction after projecting with di erent order quasi- interpolation schemes. With k = 2 the reconstruction is, on average, within one grey-scale value of the input image. #a #b Mean Std Dvtn jMax Errorj O(P a) O(P b)

1993

Cited by 1

### Table 1. Normalized RMS errors.

"... In PAGE 6: ... 5, we used 100 data randomly sampled. According to Table1 , the quasi- interpolants generates a reasonable approximation as good as global approximation for smooth functional curve re- gardless of type of the test functions where 5, 9 and 17 are the number of the control points. We note that the shape of the quasi-interpolants looks better than one of the global approximation for the step function, while the RMS error Table 1.... ..."

### Table 2. Single-row Joint Tension Testing Summary

"... In PAGE 7: ... A non- uniform distribution of the load between fasteners would partially attribute to the strength reduction for the elevated temperature test specimens. A summary of the single row joint test results is presented in Table2 . With an increase in test temperature from room to 350oF, a 37% decrease in the specimen strength capacity was observed.... ..."

### Table 2. Single-row Joint Tension Testing Summary

"... In PAGE 7: ... A non- uniform distribution of the load between fasteners would partially attribute to the strength reduction for the elevated temperature test specimens. A summary of the single row joint test results is presented in Table2 . With an increase in test temperature from room to 350oF, a 37% decrease in the specimen strength capacity was observed.... ..."

### Table 4: Normalized KI: Edge-cracked plate under tension

"... In PAGE 64: ... 33b). In Table4 , the normalized mode I stress intensity factors for both grids are presented. The reference solution for this edge-crack problem is: Kref I = p a = 2:8264 (Tada, Paris, and Irwin, 1977).... In PAGE 64: ... The reference solution for this edge-crack problem is: Kref I = p a = 2:8264 (Tada, Paris, and Irwin, 1977). From Table4 it is seen that the SIFs computed using NEM are more accurate than the cor- responding values evaluated by constant strain nite elements. Domain independence is also clearly observed for the NEM results.... ..."