Mathematical Sciences: Global Analysis and Applications

有效地求解非线性方程组这个非常普遍的问题在科学和工程的几乎每个领域都有许多重要的应用。Steven Smale和他的学生和合作者将使用几何方法，特别是牛顿的方法和路径跟踪，来研究它们与这些问题的相关性，目的是最终导致计算成本的大幅降低。

The very general problem of solving non-linear systems of equations efficiently has many important applications, in virtually every area of science and engineering. Steven Smale and his students and collaborators will use methods of geometry, especially Newton's method and path following, to study their relevance to these problems, with the aim of eventually leading to substantial reduction in costs of computation.