39 citations · 71 across the 6 of their papers we have counts for
6 papers · 1 filter
Weighted integration over a cube based on digital nets and sequences
Josef Dick, Friedrich Pillichshammer
Quasi-Monte Carlo (QMC) methods are equal weight quadrature rules to approximate integrals over the unit cube with respect to the uniform measure. In this paper we discuss QMC inte…
Toeplitz Monte Carlo
Josef Dick, Takashi Goda, Hiroya Murata
Motivated mainly by applications to partial differential equations with random coefficients, we introduce a new class of Monte Carlo estimators, called Toeplitz Monte Carlo (TMC) e…
Stability of lattice rules and polynomial lattice rules constructed by the component-by-component algorithm
Josef Dick, Takashi Goda
We study quasi-Monte Carlo (QMC) methods for numerical integration of multivariate functions defined over the high-dimensional unit cube. Lattice rules and polynomial lattice rules…
Tractability properties of the discrepancy in Orlicz norms
Josef Dick, Aicke Hinrichs, Friedrich Pillichshammer +1
We show that the minimal discrepancy of a point set in the -dimensional unit cube with respect to Orlicz norms can exhibit both polynomial and weak tractability. In particular,…
Spectral decomposition of discrepancy kernels on the Euclidean ball, the special orthogonal group, and the Grassmannian manifold
Josef Dick, Martin Ehler, Manuel Gräf +1
To numerically approximate Borel probability measures by finite atomic measures, we study the spectral decomposition of discrepancy kernels when restricted to compact subsets of $\…
Improved Efficiency of a Multi-Index FEM for Computational Uncertainty Quantification
Josef Dick, Michael Feischl, Christoph Schwab
We propose a multi-index algorithm for the Monte Carlo (MC) discretization of a linear, elliptic PDE with affine-parametric input. We prove an error vs. work analysis which allows…