### Table 1 produces cubic splines.

### Table 10. Values of the discretization sizes with cubic spline axial basis functions.

"... In PAGE 43: ... Note that in this and subsequent tables and gures, equal index limits are assumed and denoted by Nu = Nv = Nw = N. Speci c basis limits for the cubic splines are summarized in Table10 (see also, Table 1). Due to the nature of the forcing function, the Fourier limit M = 3 was su cient for resolving the circumferential behavior.... ..."

Cited by 1

### Table 11. Ratios of the absolute errors with cubic spline axial basis functions.

"... In PAGE 43: ... With the choice of cubic basis elements, an order O` (h4 x) convergence rate is expected for the method. To test this, ratios of errors as N is doubled are summarized in Table11 . It is noted that all ratios are signi cantly greater than the ratio of 16 expected for an exact O` (h4 x) method.... In PAGE 51: ... The absolute errors of the longitudinal, circumferential and transverse displacements and the ratio of these errors are reported in Tables 15 and 16, respectively. The ratios are similar to those of the time independent case shown in Table11 and con rm the O` (h4 x) convergence rate of the method. Figures 16 - 18 illustrate the true solutions of the longitudinal, circumferential, and transverse displacements, while Figures 19 - 21 depict the absolute errors associated with these displacements.... ..."

Cited by 1

### Table 2. L-shaped polygon, cubic splines

### TABLE I The quality of the registration as a function of the image interpolation spline degree. The warping function was interpolated by cubic splines.

### Table 4: Training errors and test errors from a supersmoother Supersmoother Supersmoother Cubic-spline smoother Supersmoother

1996

"... In PAGE 11: ... There are two versions of supersmoother, one uses manual bandwidth selection (MBS) and the other uses automatic bandwidth selection (ABS). Columns 1 and 2 in Table4 show the results of learning the two joint arm dynamics example by using a supersmoother. The per- formance of a supersmoother is worse than a cubic spline smoother (column 3, Table 4), but the supersmoother is computationally cheaper than a cubic spline smoother.... In PAGE 11: ... Columns 1 and 2 in Table 4 show the results of learning the two joint arm dynamics example by using a supersmoother. The per- formance of a supersmoother is worse than a cubic spline smoother (column 3, Table4 ), but the supersmoother is computationally cheaper than a cubic spline smoother. It is surprising that automatic bandwidth selection by cross-validation leads to worse performance.... ..."

Cited by 11

### Table 13. Ratios of the absolute errors with mixed linear and cubic spline axial bases.

"... In PAGE 47: ... (ii) Linear Spline Bases for uN; vN, Cubic Spline Basis for wN: To compare the performance of the fully cubic spline approximations with linear spline approximations of the longitudinal and circumferential displacements, the computations of (i) were repeated with the linear spline basis functions summarized in Table 1. The absolute errors obtained in this manner are reported in Table 12 while the ratios of these errors when the discretization levels are doubled are reported in Table13 . To attain su cient accuracy, the discretization level of N = 32 was added to the results (again, Nu = Nv = Nw = N in the reported results).... In PAGE 47: ... To attain su cient accuracy, the discretization level of N = 32 was added to the results (again, Nu = Nv = Nw = N in the reported results). The ratios in Table13 indicate an O` (h2 x) convergence rate for the method as expected with the linear spline basis (recall that the multiplying constant may cause ratios slightly less than the expected value of 4). When comparing the accuracy, and hence e ciency, of this basis choice with the fully cubic spline axial bases, it should be noted that with N = 32, the maximum over the three displacements of the absolute errors is 27 times the corresponding maximum error with N = 16 using cubic splines.... ..."

Cited by 1

### Table 5. Analytic and approximate frequencies for purely extensional modes obtained using N = 8 cubic splines.

"... In PAGE 33: ... The rst three analytic frequen- cies given by (3.14) are compared in Table5 with approximate values obtained with N = 8 cubic splines. Due to the accuracy of the method, the approximate frequencies agree with analytic values to within at least two decimal places in all three cases.... ..."

Cited by 1