in the repository
URN to cite this document: urn:nbn:de:bvb:703-epub-5636-9
Title data
Baier, Robert ; Hessel-von Molo, Mirko:
Newton's method and secant method for set-valued mappings.
Bayreuth
,
2012
![[thumbnail of baier_et_al_lssc_2012.pdf]](https://epub.uni-bayreuth.de/style/images/fileicons/application_pdf.png) |
|
||||||||
|
Download (239kB)
|
Abstract
For finding zeros or fixed points of set-valued maps, the fact that the space of convex, compact, nonempty sets of ℝ n is not a vector space presents a major disadvantage. Therefore, fixed point iterations or variants of Newton’s method, in which the derivative is applied only to a smooth single-valued part of the set-valued map, are often applied for calculations. We will embed the set-valued map with convex, compact images (i.e. by embedding its images) and shift the problem to the Banach space of directed sets. This Banach space extends the arithmetic operations of convex sets and allows to consider the Fréchet-derivative or divided differences of maps that have embedded convex images. For the transformed problem, Newton’s method and the secant method in Banach spaces are applied via directed sets. The results can be visualized as usual nonconvex sets in ℝ n .
Further data
| Item Type: | Preprint, postprint |
|---|---|
| Additional notes (visible to public): | erscheint in:
Lirkov, Ivan ; Margenov, Svetozar D. ; Waśniewski, Jerzy (Hrsg.): Large-scale scientific computing : 8th international conference, LSSC 2011, Sozopol, Bulgaria, June 6 - 10, 2011 ; revised selected papers. - Berlin , 2012 . - S. 91-98 |
| Keywords: | set-valued Newton's method; set-valued secant method; Gauß-Newton method; directed sets; embedding of convex compact sets |
| DDC Subjects: | 500 Science 500 Science > 510 Mathematics |
| Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics |
| Language: | English |
| Originates at UBT: | Yes |
| URN: | urn:nbn:de:bvb:703-epub-5636-9 |
| Date Deposited: | 28 May 2021 10:30 |
| Last Modified: | 07 Jun 2021 11:02 |
| URI: | https://epub.uni-bayreuth.de/id/eprint/5636 |
Download Statistics