An optimisation-based framework for non-classical Chebyshev approximation

非经典切比雪夫近似的基于优化的框架

• 批准号: DP180100602
• 负责人: A/Prof Julien Ugon
• 金额: $ 22.83万
• 依托单位: Deakin University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2018
• 资助国家: 澳大利亚
• 起止时间: 2018-08-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP180100602
• 关键词: optimisation; based; framework; non; classical

This project aims to solve open mathematical problems in multivariate and piecewise polynomial approximations, two directions that correspond to fundamental obstacles to extending classical approximation results. Through an innovative combination of optimisation and algebraic technique, the project intends to develop foundations for new results in approximation theory, and new insights into other areas of mathematics, most notably optimisation. The techniques and methods developed should also have significant benefits in the many disciplines where approximation problems appear, such as engineering, physics or data mining. The research outputs resulting from this project will be used in a wide range of fields to help implement programs, policies and improve decision making.

该项目旨在解决多元和分段多项式近似中的开放数学问题，这两个方向对应于扩展经典近似结果的根本障碍。通过优化和代数技术的创新组合，该项目旨在为近似理论的新成果以及对其他数学领域的新见解，特别是优化奠定基础。开发的技术和方法也应该在出现近似问题的许多学科中具有显着的优势，例如工程，物理或数据挖掘。该项目的研究成果将用于广泛的领域，以帮助实施计划，政策和改善决策。