### Table 1: Computed amount estradiol with error bounds.

"... In PAGE 24: ... The storage time for the rings was 24 hours, the concentration at the core was C0 = 17 gm?3 and the truncation levels on the in nite sums was p = q = 30. In Table1 we have listed the computed values for the amount released estradiol. We have also computed the error that occur because of the trun- cation of the in nite sums.... ..."

### Table 3: Computation time for reaching an error-bound.

"... In PAGE 19: ... This fact indicates, that the preconditioners being used require a certain regularity of the mesh in order to work e ciently. Table3 shows the positive in u- ence of using strongly irregular meshes. The absolut time which is required in order to reach a certain error-bound is decreasing if the ratio of grading is being increased.... ..."

### Table 3.6: Results of the upper bound heuristics. Relative error is computed with relation to the best known lower bound.

1997

Cited by 10

### Table 2: Measured rotation error computed by SVD and bound B M?1V. Each entry summarizes the results of 100 trials.

1995

"... In PAGE 22: ...mage displacement to the FOV. From (26), this holds also at large FOV. Experiments We have conducted synthetic experiments to verify these theoretical expectations. The re- sults appear in Table2 , where each entry summarizes 100 trials. The experiments were conducted as for those reported in Table 1; in particular the inverse depths were chosen from a uniform distribution, which decreases the average depths of the 3D points and cor- respondingly increases the rotation error.... In PAGE 22: ... The experiments were conducted as for those reported in Table 1; in particular the inverse depths were chosen from a uniform distribution, which decreases the average depths of the 3D points and cor- respondingly increases the rotation error. For this reason, in practice we expect rotation errors signi cantly smaller than those reported in Table2 . Note that in our experiments the maximum computed rotation error over all trials and all cases is 23:4 :41 radians.... ..."

Cited by 12

### Table 4: Error analysis for N = 223 and m = 28. Each Test column gives the number of correct digits in the computed factorization as produced by the a posteriori error bound.

"... In PAGE 20: ... Hence, when j(^ x0 0?^ x0)=^ x0j = O( ), the algorithm is componentwise stable in the backward sense, and this is con rmed by the a priori analysis. We found experimentally that j(^ x0 0 ? ^ x0)=^ x0j is relatively small even using standard double precision, on very ill conditioned matrices see Table4 . The table contains results related to three di erent kinds of test: (i) Test 1:... ..."

### Table 3: Computed quot;{uniform maximum pointwise error bound C p N?p for kU quot; ? u quot;k from the algorithm compared to the computed error from a ne computed Blasius solution for various values of N

"... In PAGE 7: ... We conclude from this that the values in the rst rows are realistic upper bounds for the corresponding values in the second rows. It should be noted that ratios between the values of kU quot; ? U8192 B k and 1:75 N?0:84 from Table3 , and between 1 p quot;kV quot; ? V 8192 B k and 44:8 N?0:82 from Table 4 are stabilized with growing N. It is remarkable that these realistic upper bounds are obtained by applying the simple experimental error analysis technique of the present paper to the numerical solutions generated by the above direct numerical method applied to this nonlinear system of partial di erential equations.... ..."

### Table 2 The mean error and max error for the rotation angle, computed by method 1, is presented together with the approximative bound (3.8). All values are given in degrees.

"... In PAGE 14: ... method 2 and method 3, since they compute the rotation angle in a completely di erent way and do not use a xed axis of rotation. Table2 shows that the rotation angle is most sensitive to perturbations when using the dot P2. It also indicates that a large value on the bound implies that the errors may be large.... In PAGE 14: ... To investigate the performance of method 2, similar computations were per- formed on triplets of dots. The result is shown in Table 3 and should be compared to Table 1 and Table2 . Since P2 is close to the rotation axis, using method 2 on the triplet (1; 2; 3) is almost like using method 1 on the pair (1; 3) with almost parallel u?vectors.... ..."

### Table 1 The error in the direction of the rotational axis, given in degrees for di erent pairs of dots. The computed mean error and max error is presented together with ap- proximate bounds, (3.6) and (3.12), of the maximum error.

"... In PAGE 13: ...roximate bounds, (3.6) and (3.12), of the maximum error. The results, presented in Table1 , show that the computation of the rotational axis using method 1 is most sensitive for perturbations when the dot pair P1; P3 is used. This can easily be explained by looking at Figure 2, where the vectors ui are shown for di erent dots.... In PAGE 14: ... To investigate the performance of method 2, similar computations were per- formed on triplets of dots. The result is shown in Table 3 and should be compared to Table1 and Table 2. Since P2 is close to the rotation axis, using method 2 on the triplet (1; 2; 3) is almost like using method 1 on the pair (1; 3) with almost parallel u?vectors.... ..."

### Table 2: Reduction rates and running times for the mechanical part model (7,942 triangles) with different fairness criteria and error bounds. The computational costs increase with the order of the fairness functional since larger regions have to be updated after each reduction step.

1998

"... In PAGE 6: ... As we expect, the choice of the fairness criterion has some impact on the obtainable degree of reduction for a given tolerance (cf. Table2 ). Ordering the potential edge collapses according to the dihedral angle criterion (order 2) typically leads to the least number of triangles.... ..."

Cited by 71