Newton's method in the context of gradients
Date
2007-09-24
Authors
Karatson, Janos
Neuberger, John W.
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
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.
Description
Keywords
Newton's method, Sobolev, Gradients
Citation
Karatson, J., & Neuberger, J. W. (2007). Newton's method in the context of gradients. <i>Electronic Journal of Differential Equations, 2007</i>(124), pp. 1-13.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.