Related papers: The best simultaneous approximation in linear 2-no…
Let $(B(t))_{t\in \Theta}$ with $\Theta={\mathbb Z}$ or $\Theta={\mathbb R}$ be a wide sense stationary process with discrete or continuous time. The classical linear prediction problem consists of finding an element in…
Acquiring information on spatial phenomena can be costly and time-consuming. In this context, to obtain reliable global knowledge, the choice of measurement location is a crucial issue. Space-lling designs are often used to control…
In this paper, we consider the linear direct sum of a real normed linear space with an order unit space and with a base normed space to obtain respectively a new order unit space and a new base normed space. As a consequence, we find that…
This paper deals with speeding up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each…
Given two nonempty and disjoint intersections of closed and convex subsets, we look for a best approximation pair relative to them, i.e., a pair of points, one in each intersection, attaining the minimum distance between the disjoint…
Our goal is to provide a novel method of representing 2D shapes, where each shape will be assigned a unique fingerprint - a computable approximation to a conformal map of the given shape to a canonical shape in 2D or 3D space (see page 22…
Cross-lingual semantic textual similarity systems estimate the degree of the meaning similarity between two sentences, each in a different language. State-of-the-art algorithms usually employ machine translation and combine vast amount of…
We prove that the existence of best coapproximation to any element of the normed linear space out of any one dimensional subspace and its coincidence with the best approximation to that element out of that subspace characterizes a real…
In this paper we study the best asymmetric (sometimes also called penalized or sign-sensitive) approximation in the metrics of the space $L_p$, $1\leqslant p\leqslant\infty$, of functions $f\in C^2\left([0,1]^2\right)$ with nonnegative…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
The closest point of a linear variety to an external point is found by using the equality case of an Ostrowski's type inequality. This point is given in closed form as the quotient of a (formal) and a (scalar) Gram determinant. Then, the…
In this paper, we deal with uniform spaces whose diagonal uniformity admits a basis consisting of equivalence relations. Such non-Archimedean uniform spaces are particularly interesting for applications in commutative ring theory, because…
Diophantine approximation is traditionally the study of how well real numbers are approximated by rationals. We propose a model for studying Diophantine approximation in an arbitrary totally bounded metric space where the rationals are…
In this paper we propose an algorithm for the approximate k-Nearest-Neighbors problem. According to the existing researches, there are two kinds of approximation criterion. One is the distance criteria, and the other is the recall criteria.…
Usage similarity estimation addresses the semantic proximity of word instances in different contexts. We apply contextualized (ELMo and BERT) word and sentence embeddings to this task, and propose supervised models that leverage these…
We present a parallel approximation algorithm for a class of mixed packing and covering semidefinite programs which generalize on the class of positive semidefinite programs as considered by Jain and Yao [2011]. As a corollary we get a…
We present novel, deterministic, efficient algorithms to compute the symmetries of a planar algebraic curve, implicitly defined, and to check whether or not two given implicit planar algebraic curves are similar, i.e. equal up to a…
G\"ahler ([4],[5]) introduced and investigated the notion of 2-metric spaces and 2-normed spaces in sixties. These concepts are inspired by the notion of area in two dimensional Euclidean space. In this paper, we choose a fundamentally…
We study integration and $L_2$-approximation on countable tensor products of function spaces of increasing smoothness. We obtain upper and lower bounds for the minimal errors, which are sharp in many cases including, e.g., Korobov, Walsh,…
We study an ancient problem that in a static or dynamical system, sought an optimal path, which the context always means within an extremal condition. In fact, through those discussions about this theme, we established a universal essential…