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Among the most efficient ways to integrate of a (hyper)cube are the lattice rules. There are several choices here, but probabilty the embedded lattice rules are the easiest to implement, and they have been tabulated.
It would be good to use lattice rules as an alternative for integration over a cube or (after an affine transformation) an arbitrary parallelepiped. I'm much less sure that higher-dimensions are supported, but it is easy to support arbitrary-dimensional integration on a parallelepiped (beyond $d=3000$, which is more than enough!) with a lattice rule. Interpolation is also relatively straightforward, as it is a generalization of the current structure with specially selected vectors.
The text was updated successfully, but these errors were encountered:
Among the most efficient ways to integrate of a (hyper)cube are the lattice rules. There are several choices here, but probabilty the embedded lattice rules are the easiest to implement, and they have been tabulated.
For a (simpler) lead reference, I recommend the early paper from Sloan.
It would be good to use lattice rules as an alternative for integration over a cube or (after an affine transformation) an arbitrary parallelepiped. I'm much less sure that higher-dimensions are supported, but it is easy to support arbitrary-dimensional integration on a parallelepiped (beyond$d=3000$ , which is more than enough!) with a lattice rule. Interpolation is also relatively straightforward, as it is a generalization of the current structure with specially selected vectors.
The text was updated successfully, but these errors were encountered: