A note on concatenation of quasi-Monte Carlo and plain Monte Carlo rules in high dimensions.

In this short note, we study a concatenation of quasi-Monte Carlo and plain Monte Carlo rules for high-dimensional numerical integration in weighted function spaces. In particular, we consider approximating the integral of periodic functions defined over the $s$-dimensional unit cube by using rank-1 lattice point sets only for the first $d\, (

Keywords:

• Monte Carlo method
• Applied mathematics
• Concatenation
• Unit cube
• Periodic function
• Function space
• Mathematics
• Gaussian quadrature
• Numerical integration
• Quasi-Monte Carlo method

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