78 citations · 362 across the 40 of their papers we have counts for
7 papers · 1 filter
Consistency of randomized integration methods
Julian Hofstadler, Daniel Rudolf
We prove that a class of randomized integration methods, including averages based on -sequences, Latin hypercube sampling, Frolov points as well as Cranley-Patterson rotatio…
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…
Recovery algorithms for high-dimensional rank one tensors
David Krieg, Daniel Rudolf
We present deterministic algorithms for the uniform recovery of -variate rank one tensors from function values. These tensors are given as product of univariate functions wh…
Tractability of the approximation of high-dimensional rank one tensors
Erich Novak, Daniel Rudolf
We study the approximation of high-dimensional rank one tensors using point evaluations and consider deterministic as well as randomized algorithms. We prove that for certain param…
Error bounds for computing the expectation by Markov chain Monte Carlo
Daniel Rudolf
We study the error of reversible Markov chain Monte Carlo methods for approximating the expectation of a function. Explicit error bounds with respect to different norms of the func…