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math.NA2023
Bernstein approximation and beyond: proofs by means of elementary probability theory
Tiangang Cui, Friedrich Pillichshammer
Bernstein polynomials provide a constructive proof for the Weierstrass approximation theorem, which states that every continuous function on a closed bounded interval can be unifor…
math.NA2023
Quasi-Monte Carlo methods for mixture distributions and approximated distributions via piecewise linear interpolation
Tiangang Cui, Josef Dick, Friedrich Pillichshammer
We study numerical integration over bounded regions in with respect to some probability measure. We replace random sampling with quasi-Monte Carlo methods, wh…
math.NA2023★ 1 cited
Self-reinforced polynomial approximation methods for concentrated probability densities
Tiangang Cui, Sergey Dolgov, Olivier Zahm
Transport map methods offer a powerful statistical learning tool that can couple a target high-dimensional random variable with some reference random variable using invertible tran…