Titlebar

Export bibliographic data
Literature by the same author
plus on the publication server
plus at Google Scholar

 

Newton's method and secant method for set-valued mappings

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005636
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

[img]
Format: PDF
Name: baier_et_al_lssc_2012.pdf
Version: Published Version
Available under License Creative Commons BY 4.0: Attribution
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

Downloads

Downloads per month over past year