Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 124, pp. 1-13.

Title: Newton's method in the context of gradients

Authors: Janos Karatson    (ELTE Univ., Budapest, Hungary)
         John W. Neuberger (Univ. of North Texas, Denton, TX, USA)

Abstract: 
 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.