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The implicit function theorem from Newton to the present day G. G. Magaril-Il'yaev Lomonosov Moscow State University, Faculty of Mechanics and Mathematics |
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Abstract: In 1676, I. Newton, in a letter to the Secretary of the Royal London Society, G. Oldenburg, described an iterative procedure for finding the root of a nonlinear equation, which is known today as Newton's method. Inverse or implicit function theorems are theorems on the existence of a solution to a non-linear equation, and their proofs, based on Newton's method, are natural and transparent. Moreover, this approach allows us to get more: the solution exists not only for this equation, but also for a close (in a certain sense) to it, which is important for applications when we are dealing with an approximate description of an object. Website: https://teams.microsoft.com/l/meetup-join/19%3ameeting_Nzk2ZDdjYWMtOWJlYS00MDFmLWI4ZTItM2YxZDE1ZDUwYjBj%40thread.v2/0?context=%7b%22Tid%22%3a%222ae95c20-c675-4c48-88d3-f276b762bf52%22%2c%22Oid%22%3a%22b9b023a8-1202-4361-afc9-101dc49ef4a6%22%7d |