The Mathematical Institute, University of Oxford, Eprints Archive

The continuous Newton-Raphson method can look ahead

Hauser, Raphael and Nedic, Jelena (2003) The continuous Newton-Raphson method can look ahead. Technical Report. Unspecified. (Submitted)

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Abstract

This paper is about an intriguing property of the continuous Newton-Raphson method for the minimization of a continuous objective function f: if x is a point in the domain of attraction of a strict local minimizer x* then the flux line of the Newton-Raphson flow that starts in x approaches x* from a direction that depends only on the behavior of f in arbitrarily small neighborhoods around x and x*. In fact, if F is a sufficiently benign perturbation of f on an open region D not containing x, then the two flux lines through x defined by the Newton-Raphson vector fields that correspond to f and F differ from one another only within D.

The work was supported by EPSRC grant GR/S34472 (R. Hauser) and by the Clarendon Fund, Oxford University Press and ORS Award, Universities UK (J Nedic)

Item Type:Technical Report (Technical Report)
Subjects:D - G > Global analysis, analysis on manifolds
H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1202
Deposited By:Lotti Ekert
Deposited On:18 May 2011 08:11
Last Modified:18 May 2011 08:11

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