Karatson, JanosNeuberger, John W.2021-08-172021-08-172007-09-24Karatson, J., & Neuberger, J. W. (2007). Newton's method in the context of gradients. <i>Electronic Journal of Differential Equations, 2007</i>(124), pp. 1-13.1072-6691https://hdl.handle.net/10877/14339This 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.Text13 pages1 file (.pdf)enAttribution 4.0 InternationalNewton's methodSobolevGradientsArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.