Based on the theoretical framework recently proposed by Bonifacius and Neitzel (2018) we discuss the sequential quadratic programming (SQP) method for the numerical solution of an optimal control problem governed by a ......

This paper presents a multiscale Petrov-Galerkin finite element method for time-harmonic acoustic scattering problems with heterogeneous coefficients in the high-frequency regime. We show that the method is pollution-free ......

We introduce a new Petrov-Galerkin multiscale method for the numerical approximation of the Helmholtz equation with large wave number κ in bounded domains in ℝ^d. The discrete trial and test spaces are ......

Most high-dimensional data exhibit some correlation such that data points are not distributed uniformly in the data space but lie approximately on a lower-dimensional manifold. A major problem in many data-mining applications ...

In the present paper, we consider the construction of general sparse tensor product spaces in arbitrary space dimensions when the single subdomains are of different dimensionality and the associated ansatz spaces possess ......

We provide an interpretation for the covariance of the predictive process of Bayesian Gaussian process regression as reproducing kernel of a subset of the Cameron Martin space of the prior. We demonstrate that this ......

We present a machine learning approach using the sparse grid combination technique for the forecasting of intraday foreign exchange rates. The aim is to learn the impact of trading rules used by technical analysts just ......

This study aims at introducing new algebraic multi-level solution techniques for linear systems with M-matrices. Previous optimal geometric constructions by multi-level generating systems or multi-level frames are adapted. ...

We use a sparse grid approach to discretize a multi-dimensional partial integro-differential equation (PIDE) for the deterministic valuation of European put options on Kou’s jump-diffusion processes. We employ a generalized ......

We show that the d-dimensional Haar system H^d on the unit cube I^d is a Schauder basis in the classical Besov space B^s_p,q,1(I^d), 0 < p < 1, defined by first order ......