8. Numerical experiments
Three experiments illustrate the sampling step of Theorem 6.8 and
Theorem 6.6, and the explicit transforms in Example 7.2 and
Example 7.6. The input spaces are \ell^2 and L^2(0,1),
represented numerically by finitely many coordinates. Varying that resolution tests
the sensitivity of the observed errors; these finite computations do not prove a
uniform-in-dimension theorem.
Errors are supremum errors over finite test sets, averaged over independent trials. Appendix E records the seed, sampling laws, numerical integration and evaluation procedures.