# Dimension–Adaptive Tensor–Product Quadrature

@article{Gerstner2003DimensionAdaptiveTQ, title={Dimension–Adaptive Tensor–Product Quadrature}, author={Thomas Gerstner and Michael Griebel}, journal={Computing}, year={2003}, volume={71}, pages={65-87} }

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…

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