Topics in Algebraic Spline Geometry

代数样条几何主题

• 批准号: 2482950
• 金额: --
• 依托单位: Swansea University
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2482950
• 关键词: Topics; Algebraic; Spline; Geometry

The aim of the project is to explore algebraic geometry tools for the study of approximation methods based on piecewise polynomial functions, also known as splines. Splines are a powerful tool widely used in different challenges arising in computational mathematics, such as the numerical approximation of partial differential equations (the finite element method), the parametrization of shapes in geometric modelling and computer-aided geometric design, and data science. This project will be oriented towards the theoretical aspects of the topic, we will focus on algebraic aspects of splines, their ring structure, and connections with the theory of toric varieties.

该项目的目的是探索基于分段多项式函数的近似方法的代数几何工具，也称为花朵。花键是一种在计算数学中引起的不同挑战的强大工具，例如偏微分方程的数值近似（有限元方法），几何建模中形状的参数和计算机辅助几何设计中的参数化，以及数据科学。该项目将针对该主题的理论方面，我们将重点关注花样的代数方面，它们的环结构以及与感谢您的品种理论的联系。