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Talk Abstract
Multihomogeneous and Gauss-Newton Methods

Michael Shub, IBM Watson Research Center

We generalize work of Shub and Smale on Newton and Projective Newton Methods to cover multihomogeneous systems and overdetermined systems of analytic maps. Included are the evaluation map of polynomial systems and the generalized eigenvalue problem. By understanding the disc of convergence around the fixed points points we give complexity estimates for continuation algorithms to find the zeros of systems.

This is joint work with J.P. Dedieu.

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