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DAGSTUHL
2004
13 years 6 months ago
Information-Based Nonlinear Approximation: An Average Case Setting
Nonlinear approximation has usually been studied under deterministic assumptions and complete information about the underlying functions. In the present paper we assume only partia...
Leszek Plaskota
JC
2008
128views more  JC 2008»
13 years 5 months ago
Lattice rule algorithms for multivariate approximation in the average case setting
We study multivariate approximation for continuous functions in the average case setting. The space of d variate continuous functions is equipped with the zero mean Gaussian measu...
Frances Y. Kuo, Ian H. Sloan, Henryk Wozniakowski
SIAMCO
2002
79views more  SIAMCO 2002»
13 years 5 months ago
Multiscale Singularly Perturbed Control Systems: Limit Occupational Measures Sets and Averaging
An averaging technique for nonlinear multiscale singularly perturbed control systems is developed. Issues concerning the existence and structure of limit occupational measures sets...
Vladimir Gaitsgory, Minh-Tuan Nguyen
JC
2011
102views more  JC 2011»
13 years 9 days ago
Tractability of tensor product problems in the average case setting
It has been an open problem to derive a necessary and sufficient condition for a linear tensor product problem S = {Sd} in the average case setting to be weakly tractable but not ...
Anargyros Papageorgiou, Iasonas Petras
FOCS
2004
IEEE
13 years 9 months ago
Worst-Case to Average-Case Reductions Based on Gaussian Measures
We show that finding small solutions to random modular linear equations is at least as hard as approximating several lattice problems in the worst case within a factor almost line...
Daniele Micciancio, Oded Regev