Table 7 Comparison Among U16 (4°) (lower dimension)
Related Figures (11)
Figure 1. The Coordinate Systems. Table 2. Design and Data in Dynamic System For assessing per formance of these two models, we cal- culate w; and we for y from —180 to 180 in 10-unit incre- ments and @ from —10 to 50 in 5-unit increments by both the original equations (3.1)3.7) and the approximation mod- els (3.8) and (3.9). Figure 2, (a) and (b), shows w, and w» based on (3.1)-(3.7 , and Figure 2, (c) and (d), shows w and w2 based on the approximation models. It is clear that panels (a) and (c) o f Figure 2 have a similar shape, as do panels (b) and (d). Denote by ; (2 = 1, 2) the preceding w; values obtained by Equations (3.1) and (3.7). The matrices Q, and Q2 have size 37 x 13. Let 2; stand for the preceding w; values calculated by the corresponding approximation model. We have tr( , — A,)/(Q, — Ay) = 6.3590 x 1075, Table 3. Orthogonal Design Lg(3*) Finally, the modified L, discrepancy and its measure of variation are modified from (4.2) to (4.3) with J, = [0,x) such that the projection uniformity over all subdimensions can be considered. The modified Ly discrepancy also has a formula similar to (4.1): The symmetric L, discrepancy and its measure of vari- ation are modified such that they are invariant if x; is replaced by 1 — z,; for any j,1 <j < s. The construction is based on reproducing kernel Hilbert spaces and results in the following computational formula for the symmetric Ly discrepancy: pression similar to (4.1) as follows: Table 4. Li6(4° ) and U1¢(4°) Designs Generated by Forward Procedure Table 5. U15(4°) Designs Generated by Threshold Accepting Table 6. Comparison Among U6(4°) (full dimension) Table 8. Discrepancies of Lower-Dimensional Projections of O5
