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ENTCS
2008
91views more  ENTCS 2008»
13 years 4 months ago
Newton's method and the Computational Complexity of the Fundamental Theorem of Algebra
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 n...
Prashant Batra
TYPES
2000
Springer
13 years 8 months ago
A Constructive Proof of the Fundamental Theorem of Algebra without Using the Rationals
Abstract. In the FTA project in Nijmegen we have formalized a constructive proof of the Fundamental Theorem of Algebra. In the formalization, we have first defined the (constructiv...
Herman Geuvers, Freek Wiedijk, Jan Zwanenburg
MP
2006
134views more  MP 2006»
13 years 4 months ago
Cubic regularization of Newton method and its global performance
In this paper, we provide theoretical analysis for a cubic regularization of Newton method as applied to unconstrained minimization problem. For this scheme, we prove general local...
Yurii Nesterov, Boris T. Polyak
ENTCS
2006
113views more  ENTCS 2006»
13 years 4 months ago
A Large-Scale Experiment in Executing Extracted Programs
It is a well-known fact that algorithms are often hidden inside mathematical proofs. If these proofs are formalized inside a proof assistant, then a mechanism called extraction ca...
Luís Cruz-Filipe, Pierre Letouzey
CADE
2008
Springer
14 years 4 months ago
On Automating the Calculus of Relations
Relation algebras provide abstract equational axioms for the calculus of binary relations. They name an established area of mathematics with various applications in computer scienc...
Georg Struth, Peter Höfner