Mathematical Sciences: Global Analysis and Applications

最近获得菲尔兹奖的斯梅尔将继续他的学业 在计算复杂性理论中。他将特别研究 牛顿法及其变形 方程Smale的方法是将迭代算法 动态地。该算法的实现被看作是一个 在很大程度上作为一个动力系统， 系统理论，然后用于开发估计的全球 算法的收敛速度，而不仅仅是估计 关于渐近收敛速度。

Smale, a recent Fields Medalist, will continue his studies in computational complexity theory. In particular he will study Newton's method and variations of this algorithm for solving equations. Smale's approach is to view iterative algorithms dynamically. The implementation of the algorithm is viewed to a large extent as a dynamical system and the results from dynamical systems theory are then used to develop estimates on the global speed of convergence of the algorithm rather than just estimates on the asymptotic rate of convergence.