Related papers: Error Estimates for Sparse Tensor Products of B-sp…
In this paper, {the goal is to design deterministic sampling patterns on the sphere and the rotation group} and, thereby, construct sensing matrices for sparse recovery of band-limited functions. It is first shown that random sensing…
Trimming consists of cutting away parts of a geometric domain, without reconstructing a global parametrization (meshing). It is a widely used operation in computer aided design, which generates meshes that are unfitted with the described…
In this paper we present a locally and dimension-adaptive sparse grid method for interpolation and integration of high-dimensional functions with discontinuities. The proposed algorithm combines the strengths of the generalised sparse grid…
Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit the tensor structure of function spaces and apply…
Recent years have seen considerable work on compiling sparse tensor algebra expressions. This paper addresses a shortcoming in that work, namely how to generate efficient code (in time and space) that scatters values into a sparse result…
This paper discusses the dimensions of the spline spaces over T-meshes with lower degree. Two new concepts are proposed: extension of T-meshes and spline spaces with homogeneous boundary conditions. In the dimension analysis, the key…
A sphere is a fundamental geometric object widely used in (computer aided) geometric design. It possesses rational parameterizations but no parametric polynomial parameterization exists. The present study provides an approach to the optimal…
The main result of this paper is a bi-parameter T(b) theorem for the case that b is a tensor product of two pseudo-accretive functions. In the proof, we also discuss the L^2 boundedness of different types of the b-adapted bi-parameter…
In this study, we introduce a novel family of tensor networks, termed constrained matrix product states (MPS), designed to incorporate exactly arbitrary discrete linear constraints, including inequalities, into sparse block structures.…
Bilevel optimization problems are receiving increasing attention in machine learning as they provide a natural framework for hyperparameter optimization and meta-learning. A key step to tackle these problems is the efficient computation of…
This paper focuses on defining a measure, appropriate for obtaining optimally sparse solutions to underdetermined systems of linear equations.* The general idea is the extension of metrics in n-dimensional spaces via the Cartesian product…
We outline the construction of compatible B-splines on 3D surfaces that satisfy the continuity requirements for electromagnetic scattering analysis with the boundary element method (method of moments). Our approach makes use of Non-Uniform…
This paper introduces a novel error estimator for the Proper Generalized Decomposition (PGD) approximation of parametrized equations. The estimator is intrinsically random: It builds on concentration inequalities of Gaussian maps and an…
The paper is devoted to problem of spline approximation. A new method of nodes location for curves and surfaces computer construction by means of B-splines and results of simulink-modeling is presented. The advantages of this paper is that…
In compressed sensing, a small number of linear measurements can be used to reconstruct an unknown signal. Existing approaches leverage assumptions on the structure of these signals, such as sparsity or the availability of a generative…
In this work we consider (hierarchical, Lagrange) reduced basis approximation and a posteriori error estimation for elasticity problems in affinley parametrized geometries. The essential ingredients of the methodology are: a Galerkin…
We study the problem of approximating a matrix $\mathbf{A}$ with a matrix that has a fixed sparsity pattern (e.g., diagonal, banded, etc.), when $\mathbf{A}$ is accessed only by matrix-vector products. We describe a simple randomized…
Graph sparsification is a well-established technique for accelerating graph-based learning algorithms, which uses edge sampling to approximate dense graphs with sparse ones. Because the sparsification error is random and unknown, users must…
Sparse approximations using highly over-complete dictionaries is a state-of-the-art tool for many imaging applications including denoising, super-resolution, compressive sensing, light-field analysis, and object recognition. Unfortunately,…
In this paper, we propose an algorithm for the construction of low-rank approximations of the inverse of an operator given in low-rank tensor format. The construction relies on an updated greedy algorithm for the minimization of a suitable…