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In this paper has been considered probability-one global convergence of NFPH (Newton-Fixed Point Homotopy) algorithm for system of nonlinear equations and has been proposed a probability-one homotopy algorithm to solve a regularized…
3D Gaussian Splatting is crucial for real-time novel view synthesis due to its efficiency and ability to render photorealistic images. However, building a 3D Gaussian is guided solely by photometric loss, which can result in inconsistencies…
In this paper, we propose new techniques for solving geometric optimization problems involving interpoint distances of a point set in the plane. Given a set $P$ of $n$ points in the plane and an integer $1 \leq k \leq \binom{n}{2}$, the…
A polynomial homotopy is a family of polynomial systems, where the systems in the family depend on one parameter. If for one value of the parameter we know a regular solution, then what is the nearest value of the parameter for which the…
We present a new numerical method for the isometric embedding of 2-geometries specified by their 2-metrics in three dimensional Euclidean space. Our approach is to directly solve the fundamental embedding equation supplemented by six…
Geometric consistency, i.e. the preservation of neighbourhoods, is a natural and strong prior in 3D shape matching. Geometrically consistent matchings are crucial for many downstream applications, such as texture transfer or statistical…
The data arrangement problem on regular trees (DAPT) consists in assigning the vertices of a given graph G to the leaves of a d-regular tree T such that the sum of the pairwise distances of all pairs of leaves in T which correspond to edges…
We survey theoretical, algorithmic, and computational results at the intersection of distance geometry problems and mathematical programming, both with and without adjacencies as part of the input. While mathematical programming methods can…
Several important algorithms for machine learning and data analysis use pairwise distances as input. On Riemannian manifolds these distances may be prohibitively costly to compute, in particular for large datasets. To tackle this problem,…
Numerical algebraic geometry provides a number of efficient tools for approximating the solutions of polynomial systems. One such tool is the parameter homotopy, which can be an extremely efficient method to solve numerous polynomial…
In this article, we consider nonlinear complementarity problem. We introduce a new homotopy function for finding the solution of nonlinear complementarity problem through the trajectory . We show that the homotopy path approaching the…
Delaunay Triangulation(DT) is one of the important geometric problems that is used in various branches of knowledge such as computer vision, terrain modeling, spatial clustering and networking. Kinetic data structures have become very…
Efficient trajectory optimization is essential for avoiding collisions in unstructured environments, but it remains challenging to have both speed and quality in the solutions. One reason is that second-order optimality requires calculating…
The goal of this paper is to provide computational tools able to find a solution of a system of polynomial inequalities. The set of inequalities is reformulated as a system of polynomial equations. Three different methods, two of which…
Despite being vastly ignored in the literature, coping with topological noise is an issue of increasing importance, especially as a consequence of the increasing number and diversity of 3D polygonal models that are captured by devices of…
Finding two disjoint simple paths on two given sets of points is a geometric problem introduced by Jeff Erickson. This problem has various applications in computational geometry, like robot motion planning, generating polygon etc. We will…
This paper studies the convergence difficulty of cohesive zone models in static analysis. It is shown that an inappropriate starting point of iterations in the Newton-Raphson method is responsible for the convergence difficulty. A simple,…
We present a method for solving two minimal problems for relative camera pose estimation from three views, which are based on three view correspondences of i) three points and one line and the novel case of ii) three points and two lines…
The method of monotonization of difference schemes is being considered in the paper. The method was earlier proposed by the author for stationary problems. It is investigated in the paper more profoundly. The idea of the method is to build…
Discrete choice models with social interactions or spillovers may exhibit multiple equilibria. This paper provides a systematic approach to enumerating them for a quantitative spatial model with discrete locations, social interactions, and…