Related papers: Note on Error Bound for Trace Approximation of Pro…
In this work we present an extension of the technique of the order reduction to higher perturbative approximations in an iterative fashion. The intention is also to analyze more carefully the conditions for the validity of the order…
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…
We study the general problem of extremality for metric Diophantine approximation on submanifolds of matrices. We formulate a criterion for extremality in terms of a certain family of algebraic obstructions and show that it is sharp. In…
Data-driven methods for the solution of inverse problems have become widely popular in recent years thanks to the rise of machine learning techniques. A popular approach concerns the training of a generative model on additional data to…
We develop a sharp boundary trace theory in arbitrary bounded Lipschitz domains which, in contrast to classical results, allows "forbidden" endpoints and permits the consideration of functions exhibiting very limited regularity. This is…
Given a real matrix A with n columns, the problem is to approximate the Gram product AA^T by c << n weighted outer products of columns of A. Necessary and sufficient conditions for the exact computation of AA^T (in exact arithmetic) from c…
We consider finite element approximations of unique continuation problems subject to elliptic equations in the case where the normal derivative of the exact solution is known to reside in some finite dimensional space. To give quantitative…
Computation of the trace of a matrix function plays an important role in many scientific computing applications, including applications in machine learning, computational physics (e.g., lattice quantum chromodynamics), network analysis and…
We consider a class of nonlinear elliptic problems associated with models in biophysics, which are described by the Poisson-Boltzmann equation (PBE). We prove mathematical correctness of the problem, study a suitable class of…
The aim in model order reduction is to approximate an input-output map described by a large-scale dynamical system with a low-dimensional and cheaper-to-evaluate reduced order model. While high fidelity can be achieved by a variety of…
Bobkov (J. Theoret. Probab. 18(2) (2005) 399-412) investigated an approximate de Finetti representation for probability measures, on product measurable spaces, which are symmetric under permutations of coordinates. One of the main results…
The computation of the structured pseudospectral abscissa and radius (with respect to the Frobenius norm) of a Toeplitz matrix is discussed and two algorithms based on a low rank property to construct extremal perturbations are presented.…
This paper proposes a novel technique for the approximation of strong solutions $u \in C(\overline{\Omega}) \cap W^{2,n}_\mathrm{loc}(\Omega)$ to uniformly elliptic linear PDE of second order in nondivergence form with continuous leading…
A new Goodman-Sharma type modification of the Meyer-K\"{o}nig and Zeller operator for approximation of bounded continuous functions on [0,1) is presented. We estimate the approximation error of the proposed operator and prove direct and…
We develop a theory of higher order structures in compact abelian groups. In the frame of this theory we prove general inverse theorems and regularity lemmas for Gowers's uniformity norms. We put forward an algebraic interpretation of the…
Variational inequalities play in many applications an important role and are an active research area. Optimal a priori error estimates in the natural energy norm do exist but only very few results in other norms exist. Here we consider as…
In a previous paper, I demonstrated the accuracy of simple, precessing, power ellipse (p-ellipse) approximations to orbits of low-to-moderate eccentricity in power-law potentials. Here I explore several extensions of these approximations to…
We consider a general linear parabolic problem with extended time boundary conditions (including initial value problems and periodic ones), and approximate it by the implicit Euler scheme in time and the Gradient Discretisation method in…
In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. Recently a new unfitted finite element method…
The analysis of the spectral features of a Toeplitz matrix-sequence $\left\{T_{n}(f)\right\}_{n\in\mathbb N}$, generated by a symbol $f\in L^1([-\pi,\pi])$, real-valued almost everywhere (a.e.), has been provided in great detail in the last…