Mathematical Sciences: Global Analysis and Applications

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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.