相关论文: Approximation of *weak-to-norm continuous mappings

This paper presents generalizations of semidefinite programming formulations of 1-norm optimization problems over infinite dictionaries of vectors of complex exponentials, which were recently proposed for superresolution, gridless…

We introduce several classes of set-valued maps with generalized convexity. We obtain minimax theorems for set-valued maps which satisfy the introduced properties and are not continuous, by using a fixed point theorem for weakly naturally…

In this paper, we study tractability of $L_2$-approximation of one-periodic functions from weighted Korobov spaces in the worst-case setting. The considered weights are of product form. For the algorithms we allow information from the class…

This paper develops a novel approach to necessary optimality conditions for constrained variational problems defined in generally incomplete subspaces of absolutely continuous functions. Our approach involves reducing a variational problem…

We study universal approximation of continuous functionals on compact subsets of products of Hilbert spaces. We prove that any such functional can be uniformly approximated by models that first take finitely many continuous linear…

Koopman theory studies dynamical systems in terms of operator theoretic properties of the Perron-Frobenius operator $\mathcal{P}$ and Koopman operator $\mathcal{U}$ respectively. In this paper, we derive the rates of convergence of…

This paper introduces a quasi-interpolation operator for scalar- and vector-valued finite element spaces constructed on affine, shape-regular meshes with some continuity across mesh interfaces.This operator gives optimal estimates of the…

Approximation properties of multivariate quasi-projection operators are studied in the paper. Wide classes of such operators are considered, including the sampling and the Kantorovich-Kotelnikov type operators generated by different…

We study the approximation of non-negative multi-variate couplings in the uniform norm while matching given single-variable marginal constraints.

The paper concerns the computation of the limiting coderivative of the normal-cone mapping related to $C^{2}$ inequality constraints under weak qualification conditions. The obtained results are applied to verify the Aubin property of…

In this paper, we address two main topics. First, we study the problem of minimizing the sum of a smooth function and the composition of a weakly convex function with a linear operator on a closed vector subspace. For this problem, we…

Quite recently, a new property related to norm-attaining operators has been introduced: the weak maximizing property (WMP). In this note, we define a generalised version of it considering other topologies than the weak one (mainly the…

We introduce and investigate a new notion of the theory of approximation-the so-called degenerate approximation, i.e. approximation of the function of two (and more) variables (kernel) by means of degenerate function (kernel). We apply…

This investigation seeks to establish the practicality of numerical frame approximations. Specifically, it develops a new method to approximate the inverse frame operator and analyzes its convergence properties. It is established that…

This note presents an approach to studying the iterates of a mapping whose restriction to the complement of a finite set is continuous and open. The main examples to which the approach can be applied are piecewise monotone mappings defined…

Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the…

A nonsingular real algebraic variety Y is said to have the approximation property if for every real algebraic variety X the following holds: if f:X-->Y is a C^inf map that is homotopic to a regular map, then f can be approximated in the…

This article studies sufficient conditions on families of approximating kernels which provide $N$--term approximation errors from an associated nonlinear approximation space which match the best known orders of $N$--term wavelet expansion.…

This paper addresses weak approximation for rationally connected varieties defined over the function field of a curve, especially at places of bad reduction. Our approach entails analyzing the rational connectivity of the smooth locus of…

We consider a class of operator-induced norms, acting as finite-dimensional surrogates to the L2 norm, and study their approximation properties over Hilbert subspaces of L2 . The class includes, as a special case, the usual empirical norm…