Electron. J. Diff. Eqns., Vol. 2007(2007), No. 124, pp. 1-13.

Newton's method in the context of gradients

Janos Karatson, John W. Neuberger

This paper gives a common theoretical treatment for gradient and Newton type methods for general classes of problems. First, for Euler-Lagrange equations Newton's method is characterized as an (asymptotically) optimal variable steepest descent method. Second, Sobolev gradient type minimization is developed for general problems using a continuous Newton method which takes into account a "boundary condition" operator.

Submitted August 8, 2005. Published September 24, 2007.
Math Subject Classifications: 65J15.
Key Words: Newton's method; Sobolev; gradients.

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Janos Karatson
Department of Applied Analysis, ELTE University
Budapest, H-1518 Pf. 120, Hungary
email: karatson@cs.elte.hu
John W. Neuberger
Department of Mathematics
University of North Texas
Denton, TX 76203-1430, USA
e-mail: jwn@unt.edu

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