Monte Carlo methods. Vol. 1: basics
Monte Carlo methods. Vol. 1: basics
Information-based complexity
Algorithms in C
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Explicit cost bounds of algorithms for multivariate tensor product problems
Journal of Complexity
Journal of Computational Physics
Weighted tensor product algorithms for linear multivariate problems
Journal of Complexity
Dynamic Programming
Classification with sparse grids using simplicial basis functions
Intelligent Data Analysis
Sparse grid collocation schemes for stochastic natural convection problems
Journal of Computational Physics
Cubature formulas for function spaces with moderate smoothness
Journal of Complexity
The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications
Journal of Computational Physics
Journal of Computational Physics
A domain adaptive stochastic collocation approach for analysis of MEMS under uncertainties
Journal of Computational Physics
Multi-element probabilistic collocation method in high dimensions
Journal of Computational Physics
ACC'09 Proceedings of the 2009 conference on American Control Conference
Journal of Computational Physics
Dimension-wise integration of high-dimensional functions with applications to finance
Journal of Complexity
Finite Elements in Analysis and Design
Adaptive sparse polynomial chaos expansion based on least angle regression
Journal of Computational Physics
Structural and Multidisciplinary Optimization
Characterization of discontinuities in high-dimensional stochastic problems on adaptive sparse grids
Journal of Computational Physics
Grounding studies in a medium voltage DC shipboard power system with uncertain parameters
Proceedings of the 2010 Conference on Grand Challenges in Modeling & Simulation
Galerkin Methods for Stochastic Hyperbolic Problems Using Bi-Orthogonal Polynomials
Journal of Scientific Computing
Simulation-based optimal Bayesian experimental design for nonlinear systems
Journal of Computational Physics
An adaptive dimension decomposition and reselection method for reliability analysis
Structural and Multidisciplinary Optimization
Numerical quadrature for high-dimensional singular integrals over parallelotopes
Computers & Mathematics with Applications
Grid and basis adaptive polynomial chaos techniques for sensitivity and uncertainty analysis
Journal of Computational Physics
Scientific Programming - A New Overview of the Trilinos Project --Part 1
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We consider the numerical integration of multivariate functions defined over the unit hypercube. Here, we especially address the high-dimensional case, where in general the curse of dimension is encountered. Due to the concentration of measure phenomenon, such functions can often be well approximated by sums of lower-dimensional terms. The problem, however, is to find a good expansion given little knowledge of the integrand itself.The dimension-adaptive quadrature method which is developed and presented in this paper aims to find such an expansion automatically. It is based on the sparse grid method which has been shown to give good results for low- and moderate-dimensional problems. The dimension-adaptive quadrature method tries to find important dimensions and adaptively refines in this respect guided by suitable error estimators. This leads to an approach which is based on generalized sparse grid index sets. We propose efficient data structures for the storage and traversal of the index sets and discuss an efficient implementation of the algorithm.The performance of the method is illustrated by several numerical examples from computational physics and finance where dimension reduction is obtained from the Brownian bridge discretization of the underlying stochastic process.