Optimal algorithms for numerical integration: a survey
Sprache des Vortragstitels:
Englisch
Original Tagungtitel:
FoCM 2017, Foundations of Computational Mathematics, Barcelona, July 10th-19th, 2017
Sprache des Tagungstitel:
Englisch
Original Kurzfassung:
I will outline some recent (and several classical) results on the complexity of numerical integration using cubature rules with specific point sets. The point sets under consideration will be (admissible) lattices and digital nets, as they are the only presently known constructions that lead to optimal algorithms for the spaces considered here.
The aim of the talk is to present the state of the art in this area of research, including results in the deterministic and randomized setting, results on tractability, and numerical experiments. Additionally, we provide pointers to other relevant research areas and related open problems.
Forschungs-