A note on concatenation of quasi-Monte Carlo and plain Monte Carlo rules in high dimensions
نویسندگان
چکیده
In this note, we study a concatenation of quasi-Monte Carlo and plain Monte rules for high-dimensional numerical integration in weighted function spaces. particular, consider approximating the integral periodic functions defined over $s$-dimensional unit cube by using rank-1 lattice point sets only first $d\, (<s)$ coordinates random points remaining $s-d$ coordinates. We prove that, exploiting decay weights spaces, almost optimal order mean squared worst-case error is achieved such concatenated quadrature rule as long $d$ scales at most linearly with number points. This result might be useful extremely high dimensions, partial differential equations coefficients which even standard fast component-by-component algorithm considered computationally expensive.
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ژورنال
عنوان ژورنال: Journal of Complexity
سال: 2022
ISSN: ['1090-2708', '0885-064X']
DOI: https://doi.org/10.1016/j.jco.2022.101647