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On weak tractability of the Clenshaw-Curtis Smolyak algorithm. (English) Zbl 1295.41028

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.

MSC:

41A55 Approximate quadratures
65D30 Numerical integration
26E05 Real-analytic functions
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