We study the information complexity of the numerical integration on the H¨older-Nikolskii classes MHrp in the randomized setting. We adopt classical Monte Carlo method to approximate this integration and derive the corresponding convergence rate. Comparing our results with the previous known results in the deterministic setting, we see that the randomized algorithms have faster convergence rates.
Digital Object Identifier (DOI)
Liqin, Duan and Peixin, Ye
"Complexity of the Integration on H?lder-Nikolskii Classes with Mixed Smoothness,"
Applied Mathematics & Information Sciences: Vol. 10
, Article 37.
Available at: https://dc.naturalspublishing.com/amis/vol10/iss1/37