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Measures minimizing regularized dispersion

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Academic year: 2021

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Fig. 2 Left: optimal design mesure ξ m q,∗ (smoothed density). Right: d(ξ m q,∗ ,z; µ N ) as a function of z and value of φ q q (ξ m q,∗ ; µ N ) (dashed line)
Fig. 5 Left: efficiency ( φ ˆ q ∗ ) q /φ q q (µ (r) ) as a function of r ∈ [0, 1] when d = 3, for q = 1/2 (solid line) and q = 3/2 (dashed line)
Fig. 6 Optimal density ω ξ q,∗ (dr)/(dr d−1 ) for d = 3: left for q = 2 (solid line) and q = 2.1 (dashed line); right for q = 2.25 (solid line) and q = 2.5 (dashed line).
Figure 7 shows the 100-point designs generated by (20) with X 1 = {(1/2,1/2)} for q = 1 (left) and q = 3/2 (right), illustrating the better space-filling behaviour of the design generated when q increases.
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