Information-based complexity
On approximate recovery of functions with bounded mixed derivative
Journal of Complexity - Festschrift for Joseph F. Traub, Part 1
Average case complexity of linear multivariate problems II: applications
Journal of Complexity
Explicit cost bounds of algorithms for multivariate tensor product problems
Journal of Complexity
Weighted tensor product algorithms for linear multivariate problems
Journal of Complexity
Worst case complexity of multivariate Feynman-Kac path integration
Journal of Complexity
On the complexity of parabolic initial-value problems with variable drift
Journal of Complexity - Special issue: Algorithms and complexity for continuous problems Schloss Dagstuhl, Germany, September 2004
On the power of standard information for multivariate approximation in the worst case setting
Journal of Approximation Theory
On the complexity of parabolic initial-value problems with variable drift
Journal of Complexity - Special issue: Algorithms and complexity for continuous problems Schloss Dagstuhl, Germany, September 2004
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We investigate the applicability of Smolyak's algorithm to tensor product problems on certain Banach spaces of multivariate functions. First, we show that the algorithm can be efficiently used for the integration problem on these function classes. For approximation problems on the Sobolev space W1,γr1,...,rd we prove that the algorithm is applicable as well; the range spaces can be any Banach spaces of functions, provided that the tensor product of these spaces is natural. On the other hand, if the range spaces are the univariate smooth function classes Cγkrk, the same conclusion can be drawn for approximation problems on any natural tensor products of Banach spaces of functions. Applications are illustrated for the integration problem on Wpr1,...,rd([0, 1]d).