Component-by-component constructions achieve the optimal rate of convergence for multivariate integration in weighted Korobov and Sobolev spaces

Theory of reproducing kernels

N. Aronszajn · Transactions of the American Mathematical Society · 1950 · 5.4K citations · Full text

Natural Sciences, Mathematics, Computational Geometry +9

When Are Quasi-Monte Carlo Algorithms Efficient for High Dimensional Integrals?

Ian H. Sloan, Henryk Woźniakowski · Journal of Complexity · 1998 · 630 citations · Full text

Computing, Computer Science, Mathematics +9

Component-by-component construction of good lattice rules

Ian H. Sloan · Mathematics of Computation · 2001 · 144 citations · Full text

Natural Sciences, Mathematics, Algorithms +4

Constructing Randomly Shifted Lattice Rules in Weighted Sobolev Spaces

Ian H. Sloan, Frances Y. Kuo, Stephen Joe · SIAM Journal on Numerical Analysis · 2002 · 138 citations

Natural Sciences, Mathematics, Algorithms +10

Tractability of Multivariate Integration for Weighted Korobov Classes

Ian H. Sloan, Henryk Woźniakowski · Journal of Complexity · 2001 · 137 citations

Natural Sciences, Mathematics, Optimization +4