Work

An Algorithm Based on Compute Unified Device Architecture for Estimating Covering Functionals of Convex Bodies

Year: 2024

Type: article

Abstract: In Chuanming Zong’s program to attack Hadwiger’s covering conjecture, which is a longstanding open problem from Convex and Discrete Geometry, it is essential to estimate covering functionals of convex bodies effectively. Recently, He et al. and Yu et al. provided two deterministic global optimization algorithms having high computational complexity for this purpose. Since satisfactory estimations of covering functionals will be sufficient in Zong’s program, we propose a stochastic global optimization algorithm based on CUDA and provide an error estimation for the algorithm. The accuracy of our algorithm is tested by comparing numerical and exact values of covering functionals of convex bodies including the Euclidean unit disc, the three-dimensional Euclidean unit ball, the regular tetrahedron, and the regular octahedron. We also present estimations of covering functionals for the regular dodecahedron and the regular icosahedron.

Source: Axioms

DOI: 10.3390/axioms13020132

Authors: Xiangyang Han, Senlin Wu, Longzhen Zhang

Institution: North University of China

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,728

Funders: National Natural Science Foundation of China, North University of China