# Approximate and integrate: Variance reduction in Monte Carlo integration via function approximation

@article{Nakatsukasa2018ApproximateAI, title={Approximate and integrate: Variance reduction in Monte Carlo integration via function approximation}, author={Y. Nakatsukasa}, journal={arXiv: Numerical Analysis}, year={2018} }

Classical algorithms in numerical analysis for numerical integration (quadrature/cubature) follow the principle of approximate and integrate: the integrand is approximated by a simple function (e.g. a polynomial), which is then integrated exactly. In high-dimensional integration, such methods quickly become infeasible due to the curse of dimensionality. A common alternative is the Monte Carlo method (MC), which simply takes the average of random samples, improving the estimate as more and more… Expand

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