Smale's Fundamental Theorem of Algebra reconsidered

Details Smale's Fundamental Theorem of Algebra reconsidered Smale's Fundamental Theorem of Algebra reconsidered

2012-03-30

arxiv.org/abs/1204.0036v1

Mathematics

Numerical Analysis

28 pages, 3 figures

Scientific paper

In his 1981 Fundamental Theorem of Algebra paper Steve Smale initiated the
complexity theory of finding a solution of polynomial equations of one complex
variable by a variant of Newton's method. In this paper we reconsider his
algorithm in the light of work done in the intervening years. Our main theorem
raises more problems than it solves.

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