8 citations · 15 across the 8 of their papers we have counts for
12 papers
Sharp bounds for non-adaptive randomized approximation of high-dimensional vectors
Robert J. Kunsch, Marcin Wnuk
We study the complexity of approximating the finite-dimensional vector space embedding for based on non-adaptive rand…
Adaptive and non-adaptive randomized approximation of high-dimensional vectors
Robert J. Kunsch, Marcin Wnuk
We study approximation of the embedding , , based on randomized algorithms that use up to arbitrary linear function…
Uniform approximation of vectors using adaptive randomized information
Robert J. Kunsch, Marcin Wnuk
We study approximation of the embedding , , based on randomized adaptive algorithms that use arbitrary linear functionals as…
Linear Monte Carlo quadrature with optimal confidence intervals
Robert J. Kunsch
We study the numerical integration of functions from isotropic Sobolev spaces using finitely many function evaluations within randomized algorithms, aiming for the…
Randomized approximation of summable sequences -- adaptive and non-adaptive
Robert Kunsch, Erich Novak, Marcin Wnuk
We prove lower bounds for the randomized approximation of the embedding based on algorithms that use arbitrary linear (hence non-adaptive) info…
Expected dispersion of uniformly distributed points
Aicke Hinrichs, David Krieg, Robert J. Kunsch +1
The dispersion of a point set in is the volume of the largest axis parallel box inside the unit cube that does not intersect with the point set. We study the expected dis…
Optimal confidence for Monte Carlo integration of smooth functions
Robert J. Kunsch, Daniel Rudolf
We study the complexity of approximating integrals of smooth functions at absolute precision with confidence level . The optimal error rate for mu…
Solvable Integration Problems and Optimal Sample Size Selection
Robert J. Kunsch, Erich Novak, Daniel Rudolf
We compute the integral of a function or the expectation of a random variable with minimal cost and use, for our new algorithm and for upper bounds of the complexity, i.i.d. sample…
The Difficulty of Monte Carlo Approximation of Multivariate Monotone Functions
Robert J. Kunsch
We study the -approximation of -variate monotone functions based on information from function evaluations. It is known that this problem suffers from the curse of dimen…
Breaking the Curse for Uniform Approximation in Hilbert Spaces via Monte Carlo Methods
Robert J. Kunsch
We study the -approximation of -variate functions from Hilbert spaces via linear functionals as information. It is a common phenomenon in tractability studies that u…
Monte Carlo Methods for Uniform Approximation on Periodic Sobolev Spaces with Mixed Smoothness
Glenn Byrenheid, Robert J. Kunsch, Van Kien Nguyen
We consider the order of convergence for linear and nonlinear Monte Carlo approximation of compact embeddings from Sobolev spaces of dominating mixed smoothness defined on the toru…
High-Dimensional Function Approximation: Breaking the Curse with Monte Carlo Methods
Robert J. Kunsch
In this dissertation we study the tractability of the information-based complexity for -variate function approximation problems. In the deterministic setting…