Information-based complexity
Explicit cost bounds of algorithms for multivariate tensor product problems
Journal of Complexity
Algorithm 698: DCUHRE: an adaptive multidemensional integration routine for a vector of integrals
ACM Transactions on Mathematical Software (TOMS)
Journal of Computational and Applied Mathematics
When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
Journal of Complexity
Weighted tensor product algorithms for linear multivariate problems
Journal of Complexity
Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates
Mathematics and Computers in Simulation - IMACS sponsored Special issue on the second IMACS seminar on Monte Carlo methods
Constructing Randomly Shifted Lattice Rules in Weighted Sobolev Spaces
SIAM Journal on Numerical Analysis
The Path Integral Approach to Financial Modeling and Options Pricing
Computational Economics
The effective dimension and quasi-Monte Carlo integration
Journal of Complexity
Why Are High-Dimensional Finance Problems Often of Low Effective Dimension?
SIAM Journal on Scientific Computing
On the approximation error in high dimensional model representation
Proceedings of the 40th Conference on Winter Simulation
Smoothness and dimension reduction in Quasi-Monte Carlo methods
Mathematical and Computer Modelling: An International Journal
Characterization of discontinuities in high-dimensional stochastic problems on adaptive sparse grids
Journal of Computational Physics
Error Estimates for the ANOVA Method with Polynomial Chaos Interpolation: Tensor Product Functions
SIAM Journal on Scientific Computing
Enhancing Quasi-Monte Carlo Methods by Exploiting Additive Approximation for Problems in Finance
SIAM Journal on Scientific Computing
An adaptive dimension decomposition and reselection method for reliability analysis
Structural and Multidisciplinary Optimization
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We present a new general class of methods for the computation of high-dimensional integrals. The quadrature schemes result by truncation and discretization of the anchored-ANOVA decomposition. They are designed to exploit low effective dimensions and include sparse grid methods as special case. To derive bounds for the resulting modelling and discretization errors, we introduce effective dimensions for the anchored-ANOVA decomposition. We show that the new methods can be applied in locally adaptive and dimension-adaptive ways and demonstrate their efficiency by numerical experiments with high-dimensional integrals from finance.