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Newton's method and the computational complexity of the fundamental theorem of algebra
Citation Link: https://doi.org/10.15480/882.2329
Publikationstyp
Journal Article
Date Issued
2008-03-21
Sprache
English
Author(s)
Institut
TORE-DOI
TORE-URI
Volume
202
Start Page
201
End Page
218
Citation
Electronic Notes in Theoretical Computer Science (202): 201-218 (2008)
Publisher DOI
Scopus ID
Publisher
Elsevier Science
Several different uses of Newton's method in connection with the Fundamental Theorem of Algebra are pointed out. Theoretical subdivision schemes have been combined with the numerical Newton iteration to yield fast root-approximation methods together with a constructive proof of the fundamental theorem of algebra. The existence of the inverse near a simple zero may be used globally to convert topological methods like path-following via Newton's method to numerical schemes with probabilistic convergence. Finally, fast factoring methods which yield root-approximations are constructed using some algebraic Newton iteration for initial factor approximations.
Subjects
subdivision schemes
global methods
factorization approach
constructive proofs
DDC Class
510: Mathematik
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