A universal cubature formula for functions with mixed smoothness
Sprache des Vortragstitels:
Englisch
Original Tagungtitel:
The 8th International Congress on Industrial and Applied Mathematics
Sprache des Tagungstitel:
Englisch
Original Kurzfassung:
We prove upper bounds on the order of convergence of Frolov?s
cubature formula for numerical integration in function spaces of dominating
mixed smoothness on the unit cube. More precisely, we study worst-case integration
errors for Besov and Triebel-Lizorkin spaces, and our results treat
the whole range of admissible parameters. In particular, we study the effect
of small smoothness. (Joint work with Tino Ullrich, HCM Bonn)