Scientific Computing and the Chebfun System

科学计算和 Chebfun 系统

• 批准号: EP/E045847/1
• 负责人: Lloyd Trefethen
• 金额: $ 46.42万
• 依托单位: University of Oxford
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2007
• 资助国家: 英国
• 起止时间: 2007 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FE045847%2F1
• 关键词: Scientific; Computing; Chebfun; System

MATLAB has become the primary mathematical programming language for hundreds of thousands of engineers and scientists around the world. This proposal seeks funding to pursue an exciting opportunity to extend MATLAB in a fundamental way. This project is believed to be unique, with no competitors anywhere so far.Computing systems such as Maple and Mathematica can solve some mathematical problems symbolically, delivering exact answers in special cases. However, for scientific computing and computational science, the fraction of problems that have exact solutions is very small. That is why we compute numerically and will continue to do so. Ordinarily, numerical computation is carried out with numbers. The chebfun system realizes a new vision: numerical computation with functions. We seek funding to extend this system in fundamental ways and bring it closer to scientific applications.

MATLAB已经成为全世界数十万工程师和科学家的主要数学编程语言。该提案寻求资金，以寻求一个令人兴奋的机会，从根本上扩展MATLAB。这个项目被认为是独一无二的，到目前为止在任何地方都没有竞争对手。Maple和Mathematica等计算系统可以象征性地解决一些数学问题，在特殊情况下提供精确的答案。然而，对于科学计算和计算科学，具有精确解的问题的比例非常小。这就是为什么我们用数字计算，并将继续这样做。通常，数值计算是用数字进行的。Chebfun系统实现了一个新的愿景：用函数进行数值计算。我们寻求资金，从根本上扩展这一系统，使其更接近科学应用。

项目成果

How fast do radial basis function interpolants of analytic functions converge?

解析函数的径向基函数插值收敛的速度有多快？

• DOI: 10.1093/imanum/drq020
• 发表时间: 2011
• 期刊: IMA Journal of Numerical Analysis
• 影响因子: 2.1
• 作者: Platte R