相关论文: The Area Method in the Wolfram Language

The Euclidean Median (EM) of a set of points $\Omega$ in an Euclidean space is the point x minimizing the (weighted) sum of the Euclidean distances of x to the points in $\Omega$. While there exits no closed-form expression for the EM, it…

This paper explores and proves the one-seventh area triangle using a purely algebraic approach as opposed to a geometric one. A triangle set purely in the complex plane is used so that we can utilise features of the complex number system to…

Spectral Method is a commonly used scheme to cluster data points lying close to Union of Subspaces by first constructing a Random Geometry Graph, called Subspace Clustering. This paper establishes a theory to analyze this method. Based on…

We construct the differential geometry of smooth manifolds equipped with an algebraic curvature map acting as an area measure. Area metric geometry provides a spacetime structure suitable for the discussion of gauge theories and strings,…

In this article I conduct a short review of the proofs of the area inside a circle. These include intuitive as well as rigorous analytic proofs. This discussion is important not just from mathematical view point but also because…

The probabilistic method is a technique for proving combinatorial existence results by means of showing that a randomly chosen object has the desired properties with positive probability. A particularly powerful probabilistic tool is the…

In the Area Labeling Problem one is after placing the label of a geographic area. Given the outer boundary of the area and an optional set of holes. The goal is to find a label position such that the label spans the area and is conform to…

We propose a new effective method called spherical authalic energy minimization (SAEM) for computing spherical area-preserving parameterizations of genus-zero surfaces. The proposed SAEM has solid theoretical support and guaranteed…

The variational local moment approach (V-LMA), being a modification of the method due to Logan {\it et al}., is presented here. The existence of local moments is taken from the outset and their values are determined through variational…

The trust region method is an algorithm traditionally used in the field of derivative free optimization. The method works by iteratively constructing surrogate models (often linear or quadratic functions) to approximate the true objective…

Linear discriminant analysis (LDA) is a widely used algorithm in machine learning to extract a low-dimensional representation of high-dimensional data, it features to find the orthogonal discriminant projection subspace by using the Fisher…

A computation method of algebraic local cohomology with parameters, associated with zero-dimensional ideal with parameter, is introduced. This computation method gives us in particular a decomposition of the parameter space depending on the…

This paper presents a new algorithm based on interval methods for rigorously constructing inner estimates of feasible parameter regions together with enclosures of the solution set for parameter-dependent systems of nonlinear equations in…

The Lov\'{a}sz Local Lemma is a very powerful tool in probabilistic combinatorics, that is often used to prove existence of combinatorial objects satisfying certain constraints. Moser and Tardos have shown that the LLL gives more than just…

In this paper we presented the modified algorithm for astrometric reduction of the wide-field images. This algorithm is based on the iterative using of the method of ordinary least squares (OLS) and statistical Student t-criterion. The…

Due to its fractal nature, much about the area of the Mandelbrot set $M$ remains to be understood. While a series formula has been derived by Ewing and Schober to calculate the area of $M$ by considering its complement inside the Riemann…

An elementary, albeit higher dimensional, argument is used to compute the area under the power function curve between 0 and 1.

The recently proposed Broximal Point Method (BPM) [Gruntkowska et al., 2025] offers an idealized optimization framework based on iteratively minimizing the objective function over norm balls centered at the current iterate. It enjoys…

The distance geometry problem asks to find a realization of a given simple edge-weighted graph in a Euclidean space of given dimension K, where the edges are realized as straight segments of lengths equal (or as close as possible) to the…

In this paper a local approximation method on the sphere is presented. As interpolation scheme we consider a partition of unity method, such as the modified spherical Shepard's method, which uses zonal basis functions (ZBFs) plus spherical…