Newton's method in the context of gradients
| dc.contributor.author | Karatson, Janos | |
| dc.contributor.author | Neuberger, John W. | |
| dc.date.accessioned | 2021-08-17T15:49:51Z | |
| dc.date.available | 2021-08-17T15:49:51Z | |
| dc.date.issued | 2007-09-24 | |
| dc.description.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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 13 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.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. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14339 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University-San Marcos, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.holder | This work is licensed under a Creative Commons Attribution 4.0 International License. | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2007, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | Newton's method | |
| dc.subject | Sobolev | |
| dc.subject | Gradients | |
| dc.title | Newton's method in the context of gradients | |
| dc.type | Article |