INS Preprints: INS Preprints: Recent submissions
Now showing items 101-120 of 153
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ε-dimension in infinite dimensional hyperbolic cross approximation and application to parametric elliptic PDEs
(2017)In this article, we present a cost-benefit analysis of the approximation in tensor products of Hilbert spaces of Sobolev-analytic type. The Sobolev part is defined on a finite dimensional domain, whereas the analytical ... -
Low-rank approximation to heterogeneous elliptic problems
(2017-03)In this work, we investigate the low-rank approximation of elliptic problems in heterogeneous media by means of Kolmogrov <em>n</em>-width and asymptotic expansion. This class of problems arises in practical applications ... -
Second order optimality conditions for optimal control of quasilinear parabolic equations
(2017-03)We discuss an optimal control problem governed by a quasilinear parabolic PDE including mixed boundary conditions and Neumann boundary control, as well as distributed control. Second order necessary and sufficient optimality ... -
On the expected uniform error of geometric Brownian motion approximated by the Lévy-Ciesielski construction
(2017-06)It is known that the Brownian bridge or Lévy-Ciesielski construction of Brownian paths almost surely converges uniformly to the true Brownian path. In the present article the focus is on the error. In particular, we show ... -
Singular value decomposition versus sparse grids: Refined complexity estimates
(2017)We compare the cost complexities of two approximation schemes for functions which live on the product domain <em>Ω<sub>1</sub></em> × <em>Ω<sub>2</sub></em> of sufficiently smooth domains <em>Ω<sub>1</sub></em> ⊂ ... -
On the convergence rate of sparse grid least squares regression
(2017-08)While sparse grid least squares regression algorithms have been frequently used to tackle Big Data problems with a huge number of input data in the last 15 years, a thorough theoretical analysis of stability properties, ... -
A collection of nonsmooth Riemannian optimization problems
(2017-09)Nonsmooth Riemannian optimization is a still scarcely explored subfield of optimization theory that concerns the general problem of minimizing (or maximizing), over a domain endowed with a manifold structure, a real-valued ... -
A representer theorem for deep kernel learning
(2019-05)In this paper we provide a finite-sample and an infinite-sample representer theorem for the concatenation of (linear combinations of) kernel functions of reproducing kernel Hilbert spaces. These results serve as mathematical ... -
Tangent and normal cones for low-rank matrices
(2017-10)In [D. R. Luke, <em>J. Math. Imaging Vision</em>, 47(3):231-238, 2013] the structure of the Mordukhovich normal cone to varieties of low rank matrices at rank-deficient points has been determined. A simplified proof of ... -
Upscaled HDG methods for Brinkman equations with high-contrast heterogeneous coefficient
(2017-10)In this paper, we present new upscaled HDG methods for Brinkman equations in the context of high-contrast heterogeneous media. The a priori error estimates are derived in terms of both fine and coarse scale parameters that ... -
Stochastic subspace correction in Hilbert space
(2017-11)We consider an incremental approximation method for solving variational problems in infinite-dimensional separable Hilbert spaces, where in each step a randomly and independently selected subproblem from an infinite ... -
On the degree of ill-posedness of multi-dimensional magnetic particle imaging
(2017-12)Magnetic particle imaging is an imaging modality of relatively recent origin, and it exploits the nonlinear magnetization response for reconstructing the concentration of nanoparticles. Since first invented in 2005, it has ... -
Kernel-based stochastic collocation for the random two-phase Navier-Stokes equations
(2018-10)In this work, we apply stochastic collocation methods with radial kernel basis functions for an uncertainty quantification of the random incompressible two-phase Navier–Stokes equations. Our approach is nonintrusive and ... -
Optimally rotated coordinate systems for adaptive least-squares regression on sparse grids
(2018-02)For low-dimensional data sets with a large amount of data points, standard kernel methods are usually not feasible for regression anymore. Besides simple linear models or involved heuristic deep learning models, grid-based ... -
Simulation of micron-scale drop impact
(2018-10)The numerical simulation of droplet impact is of interest for a vast variety of industrial processes, where practical experiments are costly and time-consuming. In these simulations, the dynamic contact angle is a key ... -
Haar system as Schauder basis in Besov spaces: the limiting cases for 0 < p ≤ 1
(2018-09)We show that the <em>d</em>-dimensional Haar system <em>H<sup>d</sup></em> on the unit cube <em>I<sup>d</sup></em> is a Schauder basis in the classical Besov space B<em><sup>s</sup><sub>p,q,1</sub></em>(<em>I<sup>d</sup></em>), ... -
Stochastic subspace correction methods and fault tolerance
(2018-07)We present convergence results in expectation for stochastic subspace correction schemes and their accelerated versions to solve symmetric positive-definite variational problems, and discuss their potential for achieving ... -
Incremental kernel based approximations for Bayesian inverse problems
(2018-05)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 ... -
Iterated Landweber method for radial basis functions interpolation with finite accuracy
(2018-05)We consider the reconstruction of a function stemming from a reproducing kernel Hilbert space using data which is perturbed by a deterministic error of maximal size ε<sub>∞</sub>. The accuracy ε<sub>∞</sub> ... -
Sampling inequalities for anisotropic tensor product grids
(2018-04)We derive sampling inequalities for discrete point sets which are of anisotropic tensor product form. Such sampling inequalities can be used to prove convergence for arbitrary stable reconstruction processes. As usual in ...
