On weak tractability of the Clenshaw-Curtis Smolyak algorithm (Q2451171)

The authors consider the integration of \(d\)-variable (real) analytic functions \(f:[0,1]^d\to \mathbb{R}\) whose directional derivatives of all orders are bounded by one. They show that the Clenshaw-Curtis Smolyak algorithm is weakly traceable for this class of functions. The proof uses the polynomial exactness of the algorithm and an explicit bound on its operator norm.