Information-based complexity
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Monte Carlo approximation of weakly singular integral operators
Journal of Complexity
The randomized information complexity of elliptic PDE
Journal of Complexity
Optimal approximation of elliptic problems by linear and nonlinear mappings I
Journal of Complexity - Special issue: Algorithms and complexity for continuous problems Schloss Dagstuhl, Germany, September 2004
Optimal approximation of elliptic problems by linear and nonlinear mappings II
Journal of Complexity
Optimal approximation of elliptic problems by linear and nonlinear mappings III: Frames
Journal of Complexity
Sampling numbers and function spaces
Journal of Complexity
Randomized approximation of Sobolev embeddings, II
Journal of Complexity
Randomized approximation of Sobolev embeddings, II
Journal of Complexity
The randomized complexity of indefinite integration
Journal of Complexity
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We continue the study of randomized approximation of embeddings between Sobolev spaces on the basis of function values. The source space is a Sobolev space with nonnegative smoothness order; the target space has negative smoothness order. The optimal order of approximation (in some cases only up to logarithmic factors) is determined. Extensions to Besov and Bessel potential spaces are given and a problem recently posed by Novak and Wozniakowski is partially solved. The results are applied to the complexity analysis of weak solution of elliptic PDE.