Newton's method and the computational complexity of the fundamental theorem of algebra

Link:
Autor/in:
Verlag/Körperschaft:
Hamburg University of Technology
Erscheinungsjahr:
2008
Medientyp:
Text
Schlagworte:
  • subdivision schemes
  • global methods
  • factorization approach
  • constructive proofs
  • 510: Mathematik
  • 510
Beschreibung:
  • 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. © 2008 Elsevier B.V. All rights reserved.
Beziehungen:
DOI 10.1016/j.entcs.2008.03.016
Lizenzen:
  • info:eu-repo/semantics/openAccess
  • https://creativecommons.org/licenses/by-nc-nd/3.0/
Quellsystem:
TUHH Open Research
Interne Metadaten
Quelldatensatz
oai:tore.tuhh.de:11420/2925