4 papers
Quantum integration in Besov spaces with mixed smoothness
Bernd Käßemodel, Tino Ullrich
We study the complexity of high-dimensional integration of periodic functions from Besov spaces with mixed smoothness in the quantum model of computation…
Beyond Tchakaloff Quadrature: Positive Functionals, Frames and Widths
Martin Schäfer, Tino Ullrich
Tchakaloff's theorem from 1957 asserts the existence of exact quadrature rules with non-negative weights for any polynomial space of finite degree on if the underlyi…
Tent transformed order nets and quasi-Monte Carlo rules with quadratic error decay
Bernd Käßemodel, Nicolas Nagel, Tino Ullrich
We investigate the use of order digital nets for quasi-Monte Carlo quadrature of nonperiodic functions with bounded mixed second derivative over the cube. By using the so-calle…
Besov regularity of multivariate non-periodic functions in terms of half-period cosine coefficients and consequences for recovery and numerical integration
Martin Schäfer, Tino Ullrich
In the setting of -variate periodic functions, often modelled as functions on the torus , the classical tensorized Fourier system is the system of choi…