282
A. Yu. Morozov and D. L. Reviznikov
Fig. 19.5 Uncertainties in the position of bodies at different points in time
a
b
c
Fig. 19.6 Sparse grids. Hierarchical basis: a one-dimensional basis, b construction of a twodimensional basis, c two-dimensional sparse grid
ϕ(x) =
1 − |x|, x ∈ [−1, 1]
0, otherwise
Consider a set of grids G l on a unit interval [0, 1], where l is the level that defines
the width of the grid as h l = 2
−l . The grid points x l, i are specified as:
x l, i = i · h l , 0 ≤ i ≤ 2
l
.
A. Yu. Morozov and D. L. Reviznikov
Fig. 19.5 Uncertainties in the position of bodies at different points in time
a
b
c
Fig. 19.6 Sparse grids. Hierarchical basis: a one-dimensional basis, b construction of a twodimensional basis, c two-dimensional sparse grid
ϕ(x) =
1 − |x|, x ∈ [−1, 1]
0, otherwise
Consider a set of grids G l on a unit interval [0, 1], where l is the level that defines
the width of the grid as h l = 2
−l . The grid points x l, i are specified as:
x l, i = i · h l , 0 ≤ i ≤ 2
l
.