On "Upper error bounds for quadrature formulas on function classes" by K. K. Frolov

Abstract

This is a tutorial paper that gives the complete proof of a result of Frolov [2] that shows the optimal order of convergence for numerical integration of functions with bounded mixed derivatives. The presentation follows Temlyakov [8], see also [7].

11 pages

References in corpus (2)

• The role of Frolov's cubature formula for functions with bounded mixed derivative
• Optimal quasi-Monte Carlo rules on order 2 digital nets for the numerical integration of multivariate periodic functions

Cited by in corpus (4)

• Change of variable in spaces of mixed smoothness and numerical integration of multivariate functions on the unit cube
• Optimal order quadrature error bounds for infinite-dimensional higher order digital sequences
• Lattice based integration algorithms: Kronecker sequences and rank-1 lattices
• Complexity of Oscillatory Integrals on the Real Line