72065

Автор(ы): 

Автор(ов): 

2

Параметры публикации

Тип публикации: 

Статья в журнале/сборнике

Название: 

Space-filling curves for numerical approximation and visualization of solutions to systems of nonlinear inequalities with applications in robotics

ISBN/ISSN: 

0096-3003

DOI: 

10.1016/j.amc.2020.125660

Наименование источника: 

  • Applied Mathematics and Computation

Обозначение и номер тома: 

Vol. 390

Город: 

  • Амстердам

Издательство: 

  • Elsevier

Год издания: 

2021

Страницы: 

https://www.sciencedirect.com/science/article/abs/pii/S0096300320305762
Аннотация
The problem of approximating and visualizing the solution set of systems of nonlinear inequalities can be frequently met in practice, in particular, when it is required to find the working space of some robots. In this paper, a method using Peano-Hilbert space-filling curves for the dimensionality reduction has been proposed for functions satisfying the Lipschitz condition. Theoretical properties of the introduced algorithm showing advantages of this reduction in the context of the present problem have been established and convergence properties of this method have been studied. A number of experiments executed on test functions and problems regarding finding workspace of robots confirm theoretical results and show a promising character of the new methodology.

Библиографическая ссылка: 

Посыпкин М.А., Сергеев Я.Д. Space-filling curves for numerical approximation and visualization of solutions to systems of nonlinear inequalities with applications in robotics // Applied Mathematics and Computation. 2021. Vol. 390. С. https://www.sciencedirect.com/science/article/abs/pii/S0096300320305762.