相关论文: Construction of signed distance functions with an …
In this paper we present a method for constructing the continuous best fractal approximation in the space of bounded functions. We construct the finite-dimensional subspace of the space of bounded functions whose base consists of the…
The Hausdorff distance is a measure of (dis-)similarity between two sets which is widely used in various applications. Most of the applied literature is devoted to the computation for sets consisting of a finite number of points. This has…
We consider finite element approximations of ill-posed elliptic problems with conditional stability. The notion of {\emph{optimal error estimates}} is defined including both convergence with respect to mesh parameter and perturbations in…
We construct a set of $2^n$ points in $\mathbb{R}^n$ such that all pairwise Manhattan distances are odd integers, which improves the recent linear lower bound of Golovanov, Kupavskii and Sagdeev. In contrast to the Euclidean and maximum…
Mukherjee (Pattern Recognition Letters, vol. 32, pp. 824-831, 2011) recently introduced a class of distance functions called weighted t-cost distances that generalize m-neighbor, octagonal, and t-cost distances. He proved that weighted…
We prove existence of strong solutions to a family of some semilinear parabolic free boundary problems by means of elliptic regularization. Existence of solutions is obtained in two steps: we first show some uniform energy estimates and…
A new numerical method for an inverse problem for an elliptic equation with unknown potential is proposed. In this problem the point source is running along a straight line and the source-dependent Dirichlet boundary condition is measured…
We present a new approach to approximate nearest-neighbor queries in fixed dimension under a variety of non-Euclidean distances. We are given a set $S$ of $n$ points in $\mathbb{R}^d$, an approximation parameter $\varepsilon > 0$, and a…
We consider the numerical reconstruction of the spatially dependent conductivity coefficient and the source term in elliptic partial differential equations in a two-dimensional convex polygonal domain, with the homogeneous Dirichlet…
The construction of $r$-nets offers a powerful tool in computational and metric geometry. We focus on high-dimensional spaces and present a new randomized algorithm which efficiently computes approximate $r$-nets with respect to Euclidean…
We propose a novel iterative process to establish the minimum separation between two ellipsoids. The method maintains one point on each surface and updates their locations in the theta-phi parametric space. The tension along the connecting…
Consider the problem of minimizing a quadratic objective subject to quadratic equations. We study the semialgebraic region of objective functions for which this problem is solved by its semidefinite relaxation. For the Euclidean distance…
The main thrust of our current work is to exploit very specific characteristics of a given problem in order to acquire improved compactness for supercritical problems and to prove existence of new types of solutions. To this end, we shall…
This work is about ME, the Method of Ellipcenters. ME was recently introduced by these very authors as a first order accelerated scheme for unconstrained minimization. Its iterates are all centers of ellipses carefully designed to somehow…
The recent development of spectral method has been praised for its high-order convergence in simulating complex physical problems. The combination of embedded boundary method and spectral method becomes a mainstream way to tackle…
Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…
Summability has been a central object of study in difference algebra over the past half-century. It serves as a cornerstone of algebraic methods to study linear recurrences over various fields of coefficients and with respect to various…
The constrained minimization (respectively maximization) of directed distances and of related generalized entropies is a fundamental task in information theory as well as in the adjacent fields of statistics, machine learning, artificial…
A distance-squared function is one of the most significant functions in the application of singularity theory to differential geometry. In this paper, we define naturally extended mappings of distance-squared functions, wherein each…
The deformed energy method has shown to be a good option for dimensional synthesis of mechanisms. In this paper the introduction of some new features to such approach is proposed. First, constraints fixing dimensions of certain links are…