Background Approx. by Fourier Known γ Inferred γ Approx. by Function Values References
A Very Sparse Grid on [−1, 1]d
j 0 1 2 3 4 · · ·
van der Corput tj 0 1/2 1/4 3/4 1/8 · · ·
ψ(tj) := 2(tj + 1/3 mod 1) − 1 −1/3 2/3 1/6 −5/6 −1/12 · · ·
ψ(tj) := − cos(π(tj + 1/3 mod 1)) −0.5 0.8660 0.2588 −0.9659 −0.1305 · · ·
To estimate f(j), j ∈ J, use the design {(ψ(tj1
), . . . , ψ(tjd
) : j ∈ J}. E.g., for
J = {(0, 0, 0, 0), (1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0), (0, 0, 0, 1), (2, 0, 0, 0), (3, 0, 0, 0), (1, 1, 0, 0)}
Even Points ArcCos Points
· ·
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