Related papers: Dimension preserving approximation
We have built a new kind of manifolds which leads to an alternative new geometrical space. The study of the nowhere differentiable functions via a family of mean functions leads to a new characterization of this category of functions. A…
The stability result, as stated, is incorrect. In particular, the 1-dimensional extended persistence diagrams of a finely-triangulated simplicial complex X equipped with a continuous real-valued function f, and its one-skeleton graph G…
Given sufficiently many components, it is often cited that finite mixture models can approximate any other probability density function (pdf) to an arbitrary degree of accuracy. Unfortunately, the nature of this approximation result is…
We define two notions of discrete dimension based on the Minkowski and Hausdorff dimensions in the continuous setting. After proving some basic results illustrating these definitions, we apply this machinery to the study of connections…
A fractal function is a function whose graph is the attractor of an iterated function system. This paper generalizes analytic continuation of an analytic function to continuation of a fractal function.
This paper constructs a class of non-integer dimensional continuous functions with one unbounded variation point, discusses their H\"older condition and variation on their domains. Specifically, the fractal dimension of a continuous…
In recent years, the use of sparse recovery techniques in the approximation of high-dimensional functions has garnered increasing interest. In this work we present a survey of recent progress in this emerging topic. Our main focus is on the…
We study the approximation of functions which are invariant with respect to certain permutations of the input indices using flow maps of dynamical systems. Such invariant functions includes the much studied translation-invariant ones…
We study proximal random reshuffling for minimizing the sum of locally Lipschitz functions and a proper lower semicontinuous convex function without assuming coercivity or the existence of limit points. The algorithmic guarantees pertaining…
This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of…
In this paper we introduce a new family of Bernstein-type exponential polynomials on the hypercube $[0, 1]^d$ and study their approximation properties. Such operators fix a multidimensional version of the exponential function and its…
This report summarizes progress made towards a new approach for enlarging the dynamic aperture of particle accelerators. Unlike prior methods which attempted to move the location of select resonances outward in phase space, our approach…
In this paper we give a description of separating or disjointness preserving linear bijections on spaces of vector-valued absolutely continuous functions defined on compact subsets of the real line. We obtain that they are continuous and…
We introduce notions of concavity for functions on balanced polyhedral spaces, and we show that concave functions on such spaces satisfy several strong continuity properties.
This paper establishes various variational properties of parametrized versions of two convexity-preserving constructs that were recently introduced in the literature: the proximal composition of a function and a linear operator, and the…
We present an approximation scheme for functions in three dimensions, that requires only their samples on the Cartesian grid, under the assumption that the functions are sufficiently concentrated in both space and frequency. The scheme is…
Piecewise constant image approximations of sequential number of segments or clusters of disconnected pixels are treated. The method of majorizing of optimal approximation sequence by hierarchical sequence of image approximations is…
A. Rosenfeld introduced the notion of a digitally continuous function between digital images, and showed that although digital images need not have fixed point properties analogous to those of the Euclidean spaces modeled by the images,…
For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…
In this paper we extend our findings in [3] and answer further questions regarding continuity and discontinuity of seminorms on infinite-dimensional vector spaces.