Scientific Computing and the Chebfun System

MatLab已成为世界各地数十万工程师和科学家的主要数学编程语言。这项提案寻求资金，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，到目前为止还没有竞争对手。像Maple和数学这样的计算系统可以象征性地解决一些数学问题，在特殊情况下提供准确的答案。然而，对于科学计算和计算科学来说，有精确解的问题的比例很小。这就是我们进行数值计算的原因，并将继续这样做。通常情况下，数值计算是用数字来进行的。CHEBFUN系统实现了一个新的愿景：带函数的数值计算。我们寻求资金，以从根本上扩展这一系统，并使其更接近科学应用。

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.