Advanced Quasi-Monte Carlo Algorithms for High-dimensional Integration and Approximation

Henryk Woźniakowski

Kinjal Basu

Emanouil I. Atanassov, Ivan Dimov, Mariya K. Durchova

Pierre L’Ecuyer, Christiane Lemieux

Fred J. Hickernell, Thomas Müller-Gronbach, Ben Niu +1 more

Qin Li

This paper introduces the fundamental ideas of Monte Carlo methods and quasi-Monte Carlo methods and analyzes the relations between them from the perspective of algorithms, estimation of errors and convergence rates. In the paper, the author puts great emphasis on quasi-Monte Carlo methods' application on high-dimensional integration to certify the superiority of the quasi-Monte Carlo methods.