Scientific Computing and the Chebfun System

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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.