Title :
Monte Carlo integration with small random bits
Author :
Zhang, Sheng ; Ye, Peixin ; Long, Jingfan
Author_Institution :
Sch. of Math. Sci., Nankai Univ., Tianjin, China
Abstract :
Motivated by the recent progress on quantum integration, we study restricted Monte Carlo integration for anisotropic Hölder-Nikolskii classes. The results show that with c · log2 n random bits we have the same optimal order for the n-th minimal Monte Carlo integration error as with arbitrary random numbers.
Keywords :
Monte Carlo methods; error analysis; integral equations; randomised algorithms; Monte Carlo integration; anisotropic Holder-Nikolskii class; arbitrary random numbers; n-th minimal integration error; random bits; Approximation algorithms; Approximation methods; Complexity theory; Convergence; Monte Carlo methods; Polynomials; Quantum computing;
Conference_Titel :
Natural Computation (ICNC), 2010 Sixth International Conference on
Conference_Location :
Yantai, Shandong
Print_ISBN :
978-1-4244-5958-2
DOI :
10.1109/ICNC.2010.5583957
