# Overcoming the curse of dimensionality in the numerical approximation of high-dimensional semilinear elliptic partial differential equations

@article{Beck2020OvercomingTC, title={Overcoming the curse of dimensionality in the numerical approximation of high-dimensional semilinear elliptic partial differential equations}, author={Christian Beck and Lukas Gonon and Arnulf Jentzen}, journal={ArXiv}, year={2020}, volume={abs/2003.00596} }

Recently, so-called full-history recursive multilevel Picard (MLP) approximation schemes have been introduced and shown to overcome the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations (PDEs) with Lipschitz nonlinearities. The key contribution of this article is to introduce and analyze a new variant of MLP approximation schemes for certain semilinear elliptic PDEs with Lipschitz nonlinearities and to prove that the proposed… CONTINUE READING

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