Some Results on the Complexity of Numerical Integration

Abstract

This is a survey (21 pages, 124 references) written for the MCQMC 2014 conference in Leuven, April 2014. We start with the seminal paper of Bakhvalov (1959) and end with new results on the curse of dimension and on the complexity of oscillatory integrals. Some small errors of earlier versions are corrected.

References in corpus (6)

• Calculation of Discrepancy Measures and Applications
• The Curse of Dimensionality for Numerical Integration of Smooth Functions II
• Complexity of Oscillatory Integration for Univariate Sobolev Spaces
• On Weak Tractability of the Clenshaw-Curtis Smolyak Algorithm
• Computation of expectations by Markov chain Monte Carlo methods
• The weighted star discrepancy of Korobov's $p$-sets

Cited by in corpus (1)

• A note on the dispersion of admissible lattices