Related papers: Evaluating a distance function
The fundamental importance of functional differential equations has been recognized in many areas of mathematical physics, such as fluid dynamics (Hopf characteristic functional equation), quantum field theory (Schwinger-Dyson equations)…
In this paper, we present a new method for computing approximate geodesic distances. We introduce the wave method for approximating geodesic distances from a point on a manifold mesh. Our method involves the solution of two linear systems…
Very few studies involve how to construct the efficient RBFs by means of problem features. Recently the present author presented general solution RBF (GS-RBF) methodology to create operator-dependent RBFs successfully [1]. On the other…
We use discrete holomorphic polynomials to prove that, given a refining sequence of critical maps of a Riemann surface, any holomorphic function can be approximated by a converging sequence of discrete holomorphic functions.
The rarely used Hamilton-Jacobi equation has been utilized as an elegant way to find the trajectories of mechanical systems and to derive symplectic maps. Further, the exact solution in kick approximation of Hamilton's equations of motion…
In this paper we are interested in developments of elliptic functions of Jacobi. In particular a trigonometric expansion of the classical theta functions introduced by the author (Algebraic methods and q-special functions, Editors: C.R.M.…
We propose an approach for approximating the partition function which is based on two steps: (1) computing the partition function of a simplified model which is obtained by deleting model edges, and (2) rectifying the result by applying an…
Given a finite number of samples of a continuous set-valued function F, mapping an interval to compact subsets of the real line, we develop good approximations of F, which can be computed efficiently.
We consider the problem of approximating two, possibly unrelated probability distributions from a single complex-valued function $\psi$ and its Fourier transform. We show that this problem always has a solution within a specified degree of…
The transportation problem in the plane - how to move a set of objects from one set of points to another set of points in the cheapest way - is a very old problem going back several hundreds of years. In recent years the solution of the…
The paper deals with the comparison of the Gompertz function and the logistic function. We show that the Gompertz function can be approximated with high accuracy by a sum of three logistic functions (multilogistic function). Two of them are…
We propose a method for finding a cumulative distribution function (cdf) that minimizes the distance to a given cdf, while belonging to an ambiguity set constructed relative to another cdf and, possibly, incorporating soft information. Our…
A quite straightforward approximation for the electrostatic interaction between two perfectly conducting surfaces suggests itself when the distance between them is much smaller than the characteristic lengths associated to their shapes.…
This article gives an introduction for mathematicians interested in numerical computations in algebraic geometry and number theory to some recent progress in algorithmic number theory, emphasising the key role of approximate computations…
The k Nearest Neighbors (kNN) method has received much attention in the past decades, where some theoretical bounds on its performance were identified and where practical optimizations were proposed for making it work fairly well in high…
We present a systematic study of the reconstruction of a non-negative function via maximum entropy approach utilizing the information contained in a finite number of moments of the function. For testing the efficacy of the approach, we…
The minimum distance of a code is an important concept in information theory. Hence, computing the minimum distance of a code with a minimum computational cost is a crucial process to many problems in this area. In this paper, we present…
A general framework with a series of different methods is proposed to improve the estimate of convex function (or functional) values when only noisy observations of the true input are available. Technically, our methods catch the bias…
A new result in convex analysis on the calculation of proximity operators in certain scaled norms is derived. We describe efficient implementations of the proximity calculation for a useful class of functions; the implementations exploit…
We propose two efficient numerical methods of evaluating the luminosity distance in the spatially flat {\Lambda}CDM universe. The first method is based on the Carlson symmetric form of elliptic integrals, which is highly accurate and can…