On the randomized complexity of Banach space valued integration
نویسندگان
چکیده
We study the complexity of Banach space valued integration in the randomized setting. We are concerned with r-times continuously differentiable functions on the d-dimensional unit cube Q, with values in a Banach space X, and investigate the relation of the optimal convergence rate to the geometry of X. It turns out that the n-th minimal errors are bounded by cn−r/d−1+1/p if and only if X is of equal norm type p.
منابع مشابه
Complexity of Banach space valued and parametric integration
We study the complexity of Banach space valued integration. The input data are assumed to be r-smooth. We consider both definite and indefinite integration and analyse the deterministic and the randomized setting. We develop algorithms, estimate their error, and prove lower bounds. In the randomized setting the optimal convergence rate turns out to be related to the geometry of the underlying B...
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